Because it is both, we just lack the terminology to make a distinction. Judaism as a religion should be pretty clear. There exists an orthodox cannon of the Tanakh (literally an abbreviation in Hebrew of Torah, Neviim/Prophets, and Ketuvim/Writings). There is also a host of other Rabbinical and scriptural writings and philosophies.

Where I think you're more likely confused is the idea of calling it a race. Generally I don't hear people refer to it as a race so much as an ethnicity, and will continue to refer to it as such. A distinction between the two is beyond my own knowledge, but suffice it to say that an ethnicity has a little less baggage than calling it a separate race. Either way, the reason for calling it such is that Judaism through its history has been a very insular community. It is generally split between the Sephardic (Moroccan/African Jewry) and Ashkenazi (European) with smaller scattered groups. Both the Ashkenazi and Sephardic communities largely stayed very communal and over time developed a cultural and genetically influencing heritage. Just as there is a Swedish ethnicity which you can point to specific traits that would place a member within them, you can do the same with Jews. Its not just genetic by any means, but evidentially its pretty clear that you can identify certain markers. More important for Jews though is that we retain a ethnic culture that is distinct from any region that is homing us, whether that is the US, Germany, Russia, or Libya.

An analogy: almost everyone who practices Shinto is Japanese, and most Japanese practice Shinto (with varying degrees of devotion -- although most Japanese don't really have the idea that their beliefs must all be from one religion).

There are Japanese people who don't practice Shinto, of course. There are also, much more rarely, a few Shinto practitioners who aren't Japanese.

This is all pretty easy to keep track of, because "Shinto" and "Japanese" are different words.

The situation with Judaism is in some respects similar to the situation with Japanese and Shinto. Most practitioners of the religion are also members of a certain ethnic group (or perhaps family of ethnic groups, such as Ashkenazim, Sephardim, and Lembas), and large numbers of those ethnic groups practice the religion.

The difference? Basically, Jews are stuck with homonyms which make stuff confusing. It's kind of unfortunate that we don't have different words like "Japanese/Shinto," but we don't (aside from "ethnic Jew" and "religious Jew").

Update: a further complication is that traditional Rabbinical Judaism holds that the religious status of being Jewish is also heritable (through the mother). This is another aspect that is distinct from either the traditional Jewish ethnicity or from what most of us regard as religious belief. (Example: someone with three Ashkanazi Jewish grandparents, but a non-Jewish maternal grandmother, is predominantly Jewish ethnically, but does not "inherit" Jewish status according to religious law, while the child of a mother from a non-ethnically Jewish background who has converted through appropriate channels is considered by religious law to "inherit" Jewish status, even though the child might be be 0% related to "ethnic" Jews.)

Another reason is that religions are sometimes split into two categories: religions of assent, and religions of descent. In the former, one joins mostly of one's own volition, and anyone can join. This, in the list of major world religions, is composed of Christianity, Islam, and Buddhism. The latter, religions of descent, require the person to be born into their system. These are Judaism and Hinduism. Both of these have laws governing pretty strictly who is and who is not a member, and birth into the religion comes with many expectations.

^This ^theory ^is ^attributed ^to ^Paul ^Morris, ^and ^it ^can ^be ^found ^in ^the ^1998 ^Religion, ^Modernity, ^and ^Postmodernity ^by ^he ^and ^a ^few ^others

In addition to the points that others brought up, remember that Judaism is an ethnic religion, not unlike Hinduism or Shintoism. Some people might go out of their way to convert, but for the most part, Judaism is a non-proselytizing religion. That's why most Jews are able to consider themselves direct descendents of the Jews who left Jerusalem during the Diaspora.

After the Jews left Jerusalem, Jews moved to other regions, but they were very anti-assimilation. Jewish communities were very self-contained. In eastern Europe, oftentimes the local language was a second language, and Yiddish was the language which was used everyday. They didn't, for the most part, participate in the culture of their lands. A Jew in Russia was culturally more similar to a Jew in Prussia, for instance, than with a Christian Russian.

A combination of self-containment and a lack of assimilation led to the Jewish ethnicity emerging (we call it Jewish for lack of a better term, because the ethnicity has nothing to do with belief). As mentioned, these self-contained groups of Jews, which rarely intermarried, could often have similar physical traits. It also leads to a fairly homogeneous culture. Even the Ashkenazi/Sephardic split isn't a wide gap in culture given their geographic separation.

Source for much of this: I'm Jewish ethnically (not religiously), and took a course in Western Relgions, which focused mostly on Judaism, Christianity, and Islam.

For more good books on this, I suggest Paul Johnson's A History of the Jews or Simon Schama's Story of the Jews.

This article, quoting this paper may go some of the way to answering the question. I don't have access to the full article but I remember reading about it when it came out and in essence it finds that Jewish population pockets around the globe are more closely related to each other than to the populations of the places these pockets are found in, ie. a small jewish population in Iberia is more closely related to those found in Iraq than to the Iberian population. And whilst this is in some part indicitive of a recent diaspora it is still rather telling. For a long time the religious jews kept to themselves in small communities essentially remaining and retaining the race and vice versa.

Because that was how it was done 4000 years ago. Your ethnicity/people/tribe had a religion, and that was your religion. There wasn't much converting done back then.