Ok, not my forte, so I had to hit the books.

In short - there were multiple reasons for celibacy in the Catholic Church. But they were introduced early on, both on the voluntary basis, as a promotion of virtue and as an official rule within the Church in the 4th century CE, which was applicable for both monks and the clergy. It was the subject of many a theological text at the time, like the ones of St Ambrose and St Jerome. Please refer to u/udreaudsurarea 's comment for more details.

Fast forward some six centuries.

Christian Europe in the late 10th and early 11th centuries is expanding, entering one of its renaissances, spearheaded by the new, ascetic monastic orders and the prominence of the Cluny monastery, introducing vibrant new styles in worship, art, architecture, education, and changing the very image of the clergy. There were, however, certain issues that plague the church at the time. Among them were the weakened papacy, the sale of church offices to the highest bidder (simony), and the much-criticised, but common insubordination to the rules forbidding the priests to marry.

The new movements that had emerged in the monastic circles culiminated in the election of a pope who had previously been a monk - Gregory VII. The crackdown on simony and marriage among priests culminated during his papacy and has since been known as the Gregorian (or papal) reform. This turned the tide on marriage among priests, though that in itself would not be completely eliminated until centuries later, especially among the simple parish priests whose marriages tended to be fully tolerated among their congregations.

As for very pragmatic sides of celibacy - it was hard to eliminate marriage among priests, or Nicolaism, as it was called, as priests did enjoy privilige in the medieval society - their children would often follow in their father's footsteps and make careers as priests, helped by their parent's influence. While this was true on all levels of the hierarchy, sons of bishops, cardinals, and popes (oh, yes), could expect cushy positions in the society, some being escalated to powerful positions within the Church. There was no official inheritance of titles, privliges, or land, but it was there. With the new ideals taking over the in the 10th and 11th century (which was preceded by the cutely dubbed Rule of Harlots in Rome, or pornocracy, if you will), the prevalent Nicolaism was seen as a sign of moral decay within the Church.

The Investiture Controversy came a while after, though the strenghtening of papacy and its slow trek towards independence definitely stirred the pot. While the 10th century was the century of popes dependent on the whims of local aristocracy, the 11th and 12th century saw the emergence of the new issue: power within Europe.

The Holy Roman Emperor, presiding in Germany, had the power to elect the pope and nominate bishops and high-rank Church officials. The same Gregory VII was among the first to revolt against the rule, after the popes started to be nominated by a council of cardinals. The situation escalated, with popes and antipopes popping up like a weird game of whack-a-mole, across some 50 years until the culmination in 1122, when the Concordat of Worms was signed and divided the power between the pope (granting Church titles) and Emperor (granting land).

Edit: Mobile woes and fat fingers. Big thanks to u/Yara_Flor for pointing out a mistake in the text!

It's complicated!

In the Aaronic priesthood, priests were required to live in the temple, separate from their wives, during their period of service to the temple. Refraining from sexual activity was connected to the divine: Moses instructs the Israelites not to do it during his time on Mt Sinai (Exodus 19:15) and David's troops are able to take of the consecrated bread thanks to their abstinence during a war with the Philistines (1 Samuel 21:4-6). Deuteronomy 23:10–14 describes how soldiers should maintain purity in their camp so that God remains favourably disposed to them. Philo of Alexandria, a 1st century Jewish historian, wrote that Moses renounced intercourse so that he would always be ready to receive oracles from God (On the Life of Moses 2.68-2.69).

As you noted, marriage is usually seen as positive, even for priests in Judaism (the only prophet who never married, iirc, is Jeremiah). God, after all, told humanity to 'be fruitful and multiply'. However, some of the communities in Palestine around the time of the birth of Jesus may have thought differently. Josephus describes one of the three major sects of Jews in his time, the Essenes, in this manner (Wars 2.8):

The followers of the first of which are the Pharisees, of the second, the Sadducees, and the third sect, which pretends to a severer discipline, are called Essens. These last are Jews by birth, and seem to have a greater affection for one another than the other sects have. These Essens reject pleasures as an evil, but esteem continence, and the conquest over our passions to be virtue. They neglect wedlock, but choose out other persons children while they are pliable, and fit for learning, and esteem them to be of their kindred, and form them according to their own manners. They do not absolutely deny the fitness of marriage, and the succession of mankind thereby continued; but they guard against the lascivious behaviour of women, and are persuaded that none of them preserve their fidelity to one man.

Similarly, in Philo's Hypothetica (11):

And this sect of them is not an hereditary of family connexion; for family ties are not spoken of with reference to acts voluntarily performed; but it is adopted because of their admiration for virtue and love of gentleness and humanity. At all events, there are no children among the Essenes, no, nor any youths or persons only just entering upon manhood; since the dispositions of all such persons are unstable and liable to change, from the imperfections incident to their age, but they are all full-grown men, and even already declining towards old age, such as are no longer carried away by the impetuosity of their bodily passions, and are not under the influence of the appetites, but such as enjoy a genuine freedom, the only true and real liberty.

A similar, though perhaps more exoticised, account is found in Pliny (Natural History 5.15), though for reasons of length I will link to it.

We do have some texts that we think were written by this group themselves, which are known as the Dead Sea Scrolls. Here, we find evidence of a community that could be entered by voluntary submission to its rules. It contained married members and made provisions for families, with rules regulating marriage, menstrual taboos, and children. It is difficult to interpret exactly how the community was structured, however, seem to have been a celibate 'inner circle' of twelve men. They may have previously been married and had children, but then renounced marriage. The cemetery at Qumran, ascribed to this community, contains men's, women's, and children's remains. In his book Jesus, the Essenes, and Christian Origins, Simon J. Joseph describes the state of the evidence (pg 110):

[The] Qumran evidence, therefore, is ambiguous, although it is certain that the Essene movement included men, women, and children. For some Essenes, celibacy may have been temporary (CD 4.21; 1QS 1.6–11; 1QM 7.4–6). For others, it may have been lifelong. Clearly, not all Essenes were celibate, and, apart from temporary vows designed to ensure and maintain ritual purity, this may have been a matter of individual choice and voluntary decision.

There are correspondences between the style of asceticism that the Essenes are described having and some of the statements made by Jesus in the Gospels. Matthew 19:12 reads as follows:

"For there are eunuchs who have been so from birth, and there are eunuchs who have been made eunuchs by others, and there are eunuchs who have made themselves eunuchs for the sake of the kingdom of heaven. Let anyone accept this who can.”

Here he commends celibacy, but does not mandate it. Some Christians have interpreted this as recommending self-castration, but this was not Paul's take on the matter. In 1 Corinthians 7 his advice is that whoever is able should remain celibate, but for those who cannot, they should marry and avoid sin (27-28):

Are you bound to a wife? Do not seek to be free. Are you free from a wife? Do not seek a wife. But if you marry, you do not sin, and if a virgin marries, she does not sin. Yet those who marry will experience distress in the flesh, and I would spare you that.

Jesus, too, stressed that marriage is a bond that should not be broken (Matt 19:4-9), but whoever chooses to leave family and home to serve the kingdom of God will be rewarded in the world to come (Luke 18:29).

But in practice, Paul's recommendations for 'church helpers' such as deacons, elders, and bishops was that they ought to have one wife and raise their children well (1 Timothy 3, Titus 1). Apostles such as Peter do seem to have been married as well (see the narrative of the healing of his mother-in-law in Mark 1:29-31). Paul never gives us explicit information about his marital status; St. Jerome argued he had never married, but others like Martin Luther argue he would have married as per the custom of the time. So how do we get from here to mandatory lifelong celibacy for all priests?

Already in the second century, Galen noted that 'restraint from intercourse' was a custom of the Christians, and Justin Martyr held up the strict sexual code of the Christian community as a hallmark of the faith.. Tertullian (~155-220 CE), an early church father, accepted that Peter had been married. However, he argued that all other apostles had either remained virgins or become continent. He was of the opinion that sexual abstinence was the best way to achieve 'clarity of the soul'. St. Jerome (340s-420 CE) argued the same while writing against Vigilantius' defence of clerical marriage, claiming that Peter had also either stopped intercourse with his wife after he was called or that he had become a widower.

The writings of St. Ambrose, a 4th century bishop of Milan, provide some insight into the diversity of viewpoints in his time. He argued that the ordination of mrried men was acceptable, but an individual who had been elevated to the position of bishop could no longer get married and should refrain from intercourse within already-existent marriages. He noted the chastity of the priesthood of Aaron during their period of service of the temple and argued that as a result of the new Law brought by the crucifixion of Jesus, Christian priests were in perpetual service, meaning that perpetual chastity was required.

Ambrose was a major influence on the figure of St. Augustine, who as always looms large in the formation of Christian tradition. He considered sexual desire to be a mark of the Fall and a permanent reminder of humanity's sin and shame. Arguing against Jovinian, who proposed that marriage and virginity were equally good, Augustine accepted that marriage had been ordained by God and sanctified by Christ; however, while marriage was good, virginity was better. By rejecting physical passions, priests would be able to triumph over sin. In his time, it was allowed for married men to be ordained, even to high office, but then once ordaained they ought to live in continence.

The viewpoints of Jerome, Ambrose, and Augustine won out over those of Helvidius, Vigilantius, and Jovinian, and so the attitude of the former prevailed. In many Eastern churches today, married individuals can still be ordained into the clergy, but they cannot marry once ordained. Parish priests must be married and often form long-lived priestly families. /u/house_martin goes into the medieval timeline of clerical marriage so I'll direct you to their account of that, but to wrap up my own answer most priests in the Latin West too still seem to have married in the 10th century, which was followed by a series of reforms that resulted in a nominal requirement of complete clerical celibacy.

In addition to the sources I have mentioned throughout my answer, I am also drawing on Helen Parish's Clerical Celibacy in the West: c.1100-1700, which is a great source on this topic!

Can I ask… Is it permissible for a priest to adopt a child? I get that there are a variety of historical reasons for celibacy but wouldn’t adoption align well with Christian virtues of caring for those in need? Why does one never see a priest with a family that they have adopted?

I have the Catechism of the Catholic Church; Image Books, 1995: ISBN 0-385-47967-0: IMPRIMI POTEST, Joseph Cardinal Ratzinger, and in Part Two: The Celebration of the Christian Mystery, Article 6, The Sacrament of Holy Orders, describes to various aspects to Holy Orders. It commences at page 427 and ends on page 446. Paragraphs 1536 to 1600 contain the text Revelation to this topic. I don't know if this can answer the question but it can help understanding the requirements.