Basically, because the Bible wasn't written in Aramaic. The main language spoken by most people, and thus, later, most Christians, in the eastern Roman Empire, was Koine Greek, and that's what the New Testament was written in. In the west, most people (who could read) read Latin, so it was translated into Latin. Essentially, Christianity was originally a religion that used the local languages, or at least, the local lingua franca, rather than trying to make people learn a special religious language. It was only later that Latin (and, in the east, Greek) became "sacred languages". Actually, the Assyrian Church of the East does use Aramaic for its liturgy, but this is because that area originally spoke Aramaic, not Greek, so translated the New Testament back into Aramaic.

I should point out that the reason that Arabic is a kind of "sacred language" for Muslims is not because Muhammed spoke Arabic, but because the Qu'ran is written in Arabic, and so to understand its full, original meaning, its best to learn Arabic.

I would expand on /u/The_Manchurian's point in regards to the sacredness of Arabic.

Not only is the bible not written in the "sacred language" (Aramaic) in question, but the Qur'an is also not purporting to be the same kind of document that the Bible is.

The Qur'an, in the view of Muslim believers, is not merely some abstract "word of God", it is literally God's speech, perfect and eternal. The implication of that is whereas if you ask a Christian "what language does God speak?" they might reply that Jesus spoke Aramaic, and knew Hebrew, but the question of what language God the Father or God the Holy Spirit spoke is almost a non-sensical question for most Christians-- surely God the Father speaks all languages? For Muslims, there is no such doubt: God speaks Arabic.

The result of that is that while I have met plenty of Christian fundamentalists/evangelicals who believe that it is incredibly important to memorize and have as much command of the bible as possible, I have yet to meet a Christian who believes that it is important to memorize the Bible in its original languages as those languages were originally spoken. This is in contrast to the Qur'an, wherein the sacredness of God's speech means the language of the Qur'an is believed, as a matter of dogma, to be un-translateable and that, as a matter of faith, one should be able to memorize and recite the Qur'an regardless of your language of origin or whether you have any knowledge of Arabic and that it should be done in the original, classical style. So, for instance, there's a documentary that came out a while ago about the annual Egyptian international Ramadan Qur'an reciting competition which follows a number of Children from non-Arabic speaking countries and therefore have no understanding of Arabic who have flawlessly memorized the Qur'an. As far as I'm aware, nothing like this exists in the conception of a "sacred" language in Christianity or Judaism. The Catholic idea of holding a mass in Latin for which the parishioners might know the prayers in Latin but not what they mean might come close but this is clearly more extensive.

So yeah, just to add my $0.02.