It was a bit more complicated than that.

First let's explain some context- for centuries, Jews had been tarred by a stereotype of being money-grubbing and unscrupulous, which was still strongly in existence during the Civil War- and was at this point exacerbated among some in the Union with the realization that the Secretary of the Treasury of the Confederacy was a Jew with the very Jewish name of Judah P Benjamin (no Jew had ever reached such a high office in the United States). At this point, General Grant was in charge of the Department of the Tennessee (which included part of the state of Tennessee but actually included land from northern Mississippi to Illinois, from the Mississippi River to the Tennessee River. This area was being plagued by various kinds of opportunists, swindlers, smugglers and cotton speculators who were giving Grant a great deal of grief. The majority of these were not Jewish; however, given the large presence of Jews in trade in general and their easy visibility as immigrants, as well as the kinds of antisemitic sentiments not unpopular in that day, in the minds of many- including Grant- these activities were specifically associated with Jews.

Was Grant himself antisemitic? He said he wasn't, but he probably was just about as much as the average person may have been. He definitely associated the cotton speculation- a massive thorn in his side- with Jews specifically, and made multiple statements specifically casting aspersions on their honesty and demanding that they receive extra scrutiny, trying to "exclude them from the Dept." in any ways that he could, such as trying to restrict their access to the railroad. That said, only nine days before his own order expelling the Jews he had actually countermanded an order from an underling expelling "cotton-sellers, Jews, and other vagrants" from the area of Union headquarters at Holly Springs, Mississippi, as he acknowledged that cotton speculation was in fact legal for union loyalists.

While many claimed afterward that sometime in the ensuing nine days a telegram came from Washington ordering Grant to expel the Jews to prevent them from speculating, no trace of such a telegram has been found; instead, historians have found it more likely that the real catalyst was a visit from Grant's father, Jesse. Jesse Grant was a somewhat opportunistic businessman himself, to his son's chagrin, and the two had a rocky relationship. Jesse had gone into business with Jewish brothers from Cincinnati, the Macks, promising to use his clout with his son, the commander of the Department of the Tennessee, to get trading permits and have cotton shipped to New York. Grant was furious at his father's presumption and his shady tactics, and, says the editor of Grant's papers John Simon, he displaced his anger at his unscrupulous father onto the, he felt, unscrupulous Jews. Capitalizing on the fact that Jesse had been in business with Jews, and on his preexisting prejudices, Grant decided to issue the expulsion order against all Jews in the area.

Now, at the end of the day, relatively few Jews were actively expelled. The Union headquarters at Holly Springs were attacked by Confederate General Nathan Bedford Forrest within a few hours of the decree's issuance, and it therefore only spread to a few places with small Jewish populations, never reaching, for example, the relatively large Jewish community in Memphis. However, the experience for Jews being expelled from, for example, Paducah, Kentucky, was harrowing, as Jews- men, women and children- were ordered from their homes, barred from returning, in scenes that reminded many of the immigrant Jews of what they'd left behind in eastern Europe. One of the Jews who was expelled from Paducah, Cesar Kaskel, was among the many Jews who protested this measure, first by sending a telegram to President Lincoln and then, when he received no response, went to Washington himself, where he purportedly had an in person meeting. Famously, the meeting is said according to legend to have gone like this:

Lincoln: “And so, the children of Israel were driven from the happy land of Canaan?”

Kaskel: “Yes, and that is why we have come unto Father Abraham’s bosom, asking protection.”

Lincoln: “And this protection they shall have at once.”

Indeed, that is what occurred- as soon as Lincoln heard of the order, he had the general-in-chief of the Army, Henry Halleck, countermand it. Grant's mistake was in the way that he expelled Jews as a "class," to quote the order, and discriminated against them specifically; as Lincoln said later to Jewish leaders, he would hold “of no distinction between Jew and Gentile,” emphasizing that “[t]o condemn a class is, to say the least, to wrong the good with the bad. I do not like to hear a class or nationality condemned on account of a few sinners." That said, Halleck did imply to Grant that, had Grant simply expelled Jewish traders or Jewish peddlers, Lincoln may never have had a problem with it. It was the expulsion of all Jews, because they were Jews and not because of their actions (even, apparently, if those actions were merely reputed), that called for such condemnation.

The story didn't end there, because of course, six years later, Grant ran for president. The question of whether Grant, who ran as a Republican, was an antisemite became a relevant issue in the campaign; this was perhaps the first time that the Jewish community, which while less than 1% of the national population was still its largest non-Christian faith group, became a topic of discussion and had its interests noted in the campaign. Jewish Democrats, of course, such as the influential Rabbi Isaac Mayer Wise, roundly castigated Grant for his antisemitism. Jewish Republicans had a much harder choice to make, and there was a widespread effort among some of them to attempt to rehabilitate Grant's image with the help of some of Grant's campaign aides (Grant himself did not address the issue). But in the end, for the first time, a spotlight shone on Jews and their vote; of course, as we know, Grant was elected.

In office and after his tenure, in the end, Grant ended up being, as the phrase goes, good for the Jews. While Grant left the incident entirely out of his autobiography (though his wife Julia explicitly called it "obnoxious" in her own memoir), he spent his eight years in office appointing more Jews to high office than ever had been before, expressed his support for the rights of persecuted Jews in Russia and Romania, and attended the dedication ceremony for the first synagogue in Washington DC, Adas Israel, sitting through the whole three hour ceremony. In what may perhaps be a reminder for us all, he also later stated that the order “would never have been issued if it had not been telegraphed the moment it was penned, and without reflection.” He felt a real desire to repent from his previous actions and worked hard to make sure that Jews retained an equal status in American society and to prevent Christianity from becoming enshrined in United States policy- something that was easier said than done in an era when American values and Christian values were so often seen as one and the same (for an example, see my past answer about whether there was a Jewish temperance movement in the 19c). After Grant left office, levels of antisemitism apparently noticeably increased, and by the time Grant was on his deathbed he was pleased to note that Jews were among those praying for his recovery; once he died, they were among the nationwide mourners, with even Rabbi Wise, who had previously condemned Grant, noting that Grant had “often repented” of the order, deciding “that the wise also fail.”

For more on this topic, Jonathan Sarna wrote a fascinating book on this exact incident and its ramifications, When General Grant Expelled the Jews, which I highly recommend.

It seems you are asking about the background and reasons of anti-Jewish and/or anti-Semitic sentiment throughout history.

The essential point that needs to be emphasized: the reason for anti-Jewish hatred and persecution has absolutely nothing to do with things Jewish men and women did, said or thought. Religious and racial persecution is not the fault of the victim but of the persecutor and anti-Semitism, like all prejudices, is inherently irrational. Framing history in a manner that places the reason for racial hatred with its victims is a technique frequently employed by racists to justify their hateful ideology.

The reasons why Jews specifically were persecuted, expelled, and discriminated against throughout mainly European history can vary greatly depending on time and place, but there are overarching historical factors that can help us understand the historical persecution of Jews - mainly that they often were the only minority available to scapegoat.

Christian majority societies as early as the Roman empire had an often strained and complicated relationship with the Jewish population that lived within their borders. Christian leaders instituted a policy that simultaneously included grudging permissions for Jews to live in certain areas and practice their faith under certain circumstances but at the same time subjected them to discriminatory measures such as restrictions where they could live and what professions they could practice. The Christian Churches – Catholic, Orthodox, and later Protestant – also begrudgingly viewed the Jews as the people of the Old Testament but used their dominant roles in society to make the Jewish population the target of intense proselytization and other them further by preaching their fault for the death of Jesus.

This dynamic meant that Jews were the most easily recognisable and visible minority to point fingers at during a crisis. This can be best observed with the frequent accusations of "blood libel" – an anti-Semitic canard alleging that Jews murdered Christian children to use their blood in religious rituals – in situations where Christian children or adults disappeared, the communal panic immediately channeling itself as Jew-hatred with tragic results. Similarly, religious, ideological, and economic reasons were often interwoven in the expulsion of Jews to whom medieval rulers and kings owed a lot of money; in fact, one intersection of crisis-blaming and financial motive occurred during the Black Death, when local rulers were able to cynically blame Jews for the plague as an excuse for murdering and expelling them.

These processes also often took place within negotiations between social and political elites over state formation. One of the best examples is the expulsion of the Jewish population from Spain by the rulers of Castile and Aragon after the Reconquista in 1491. Expulsion and forcible conversions progressed toward an institutionalized suspicion towards so-called New Christians – Jews who’d recently converted– based on their "blood". This was an unprecedented element in antisemitic attitudes that some scholars place within the context of Spanish rulers and nobility becoming engaged in a rather brutal state formation process. In order to define themselves, they chose to define and get rid of a group they painted as alien, foreign and different in a negative way – as the "other". Once again Jews were the easily available minority.

Jews long remained in this position of only available religious minority, and over time they were often made very visible as such: discriminatory measures introduced very early on included being forced to wear certain hats and clothing, be part of humiliating rituals, pay onerous taxes, live in restricted areas of towns – ghettos – and be separated from the majority population. All this further increased the sense of “other-ness” that majority societies experienced toward the Jews. They were made into the other by such measures.

This continued with the advent of modernity, especially in the context of nationalism. The 19th century is marked by a huge shift in ways to explain the world, especially in regards to factors such as nationalism, race, and science. To break it down to the essentials: the French Revolution and its aftermath delegitimized previously established explanations for why the world was the way it was – a new paradigm of “rationalism” took hold. People would now seek to explain differences in social organizations and ways of living between the various peoples of the world with this new paradigm.

Out of this endeavour to explain why people were different soon emerged what we today understand as modern racism, meaning not just theories on why people are different but constructing a dichotomy of worth out of these differences.
A shift took place from a religious othering to one based more on nationality - and thereby, in the minds of many, on race. In the tradition of völkisch thought, as formulated by thinkers such as Gobineau and Houston Stewart Chamberlain, races as the main historical actors were seen as acting through the nation. Nations were their tool or outlet to take part in Social Darwinist competition between the races. The Jews were seen as a race without a nation - as their own race, which dates back to them being imperial subjects and older stereotypes of them as "the other" - and therefore acting internationally rather than nationally. Seen through this nationalistic lens, an individual Jew living in Germany, for example, was not seen as German but was seen as having no nation. For such Jews, this meant that the Jewish emancipation that Enlightenment brought provided unprecedented freedom and removed many of the barriers that they had previously experienced, the advent of scientific racism and volkisch thought meant that new barriers and prejudices simply replaced them.

Racist thinkers of the 19th century augmented these new barriers and prejudices with conspiratorial thinking. The best example for this anti-Semitic delusion are the Protocols of the Elders of Zion, a fake political treatise produced by the Tsarist Secret Police at some point in 1904/05 which pretends to be the minutes of a meeting of the leaders of a Jewish world conspiracy discussing plans to get rid of all the world's nations and take over the world. While the Protocols were quickly debunked as a forgery, they had a huge impact on many anti-Semitic and völkisch thinkers in Europe, including some whose writings were most likely read by the young Hitler.

The whole trope of the Jewish conspiracy as formulated by völkisch thought took on a whole new importance in the late 1910s, with the end of WWI, the Bolshevik revolution, and subsequent attempts at communist revolution in Germany and elsewhere. Jews during the 19th century had often embraced ideologies such as (classical) liberalism and communism, because they hoped these ideologies would propagate a world in which it didn’t matter whether you were a Jew or not. However, the idea of Jews being a driving force behind communism was clearly designed by Tsarist secret police and various racists in the Russian Empire as a way to discredit communism as an ideology. This trope of Jews being the main instigators behind communism and Bolshevism subsequently spread from the remnants of Tsarist Russia over the central powers all the way to Western Europe.

This delusion of an internationalist conspiracy would finally result in the Nazis’ Holocaust killing vast numbers of Jews and those made Jews by the Nazi’s racial laws. While this form of anti-Semitism lost some of its mass appeal in the years after 1945, forms of it still live on, mostly in the charge of conspiracy so central to the modern form of anti-Semitism: from instances such as the Moscow doctors’ trial, to prevalent discourses about Jews belonging to no nation, to discourses related to the Israeli-Palestinian conflict, to the recent surges of anti-Semitic violence in various states – anti-Semitism didn’t disappear after the end of the Holocaust. Even the Protocols of the Elders of Zion, the conspiratorial pamphlet debunked soon after it was written at the beginning of the 20th century, has been consistently in print throughout the world ever since.

Again, anti-Jewish persecution has never been caused by something the Jews did, said, or thought. It was and is caused by the hatred, delusions, and irrational prejudices harbored by those who carried out said persecution. After centuries of standing out due to religious and alleged racial difference, without defenders and prevented from defending themselves, Jews stood out as almost an ideal “other.” Whether the immediate cause at various points has been religious difference, conspiracy theory, ancestral memory of hatred, or simply obvious difference, Jews were and continue to be targeted by those who adhere to ideologies of hatred.

Further reading:

Amos Elon: The Pity of It All: A History of the Jews in Germany, 1743-1933. New York 2002.

Peter Pulzer: The rise of political anti-Semitism in Germany and Austria, Cambridge 1988.

Hadassa Ben-Itto: The Lie That Wouldn't Die: The Protocols of the Elders of Zion. London 2005.

Robert S. Wistrich: Antisemitism: The Longest Hatred. New York 1991.