I'm a student of philosophy studying at a small school here in Indiana. This same question appears numerous times throughout the semester and here is my thought on it.
Before there was biology, chemistry, mathematics and physics, there was philosophy. That's not to say that these weren't areas of interest to the inteligencia of the time, but it was all considered to be under the umbrella of philosophy. Through it's logical reasonings and systems of questioning/doubting, the thinkers of the time were able to use what I'll call 'philosophical inquiry' to come to conclusions in these various fields of study.
Then, there was a split between science and philosophy. I'm purposely being obscure about the time frames right now as I'm not 100% confident as to their exactness. Anyway, that split left two major branches of study: philosophy and natural science. My thought on this is that while philosophy had heretofore dealt with these matters adequately, people started to want more concrete answers to the undertakings of nature, biological process and the like. I think they felt that if they distanced the realm of the "physical" (namely, that study which lends itself to explain the physical phenonema they were questioning) from the realm of the "metaphysical" (which dealt with issues of the soul, ethics, virtues etc...) they would be better off. Which, it makes sense when viewed in the proper light that the issue of whether or not a soul exists is different than explaining why everything falls towards the center of the earth.
Then, numbers were taken out of the realm of the Aristotelian forms and brought into the realm of logical utilities. Now, we have three branches of study: philosophy, natural science and mathematics. All of which began under the umbrella of philosophy.
Fast forward a few years to the enlightenment, or the time of modern philosophers such as Descartes, Hume, Berkeley and Kant. Most of these men were very religious but became deeply disconcerted about making God responsible for everything. While not taking God completely out of the picture, they, more or less, tried to take a load off his shoulders and give explanations to such things as Causation in a more secular voice. Take Descartes for example.
Descartes was educated at the Sorbonne, one of the finest schools of the time and, coincidentally, one of the most strict Theological schools as well. After his education was complete, Descartes began his 'project of doubt.' He was concerned with what we could know that was strongly doubt resistant or completely indubitable. Among his three major things that could not be doubted was the existence of A God. He never specifies that it's a Christian God. Some people who are unable to read his works (namely, The Meditations) without taking their biased blindfolds off simply take this fact for granted. Descartes God is neither New Testament nor Old. He/She is not from the Koran or the Dhammapada, it is simply a beneficent, omniscient and omnipotent BEING who contains infinitely everything we contain finitely. Descartes also relies on God to be the gaurantor of the external world. Since he is a BOO (beneficent, omniscient, omnipotent) God, he would not fool us, according to Descartes, and make us believe there was a world external to us. This is a testament that at the advent of modern science, God still played an important part in explaining the world. While he may not be the reason everything gravitates to the center of the earth, he is the cause of everything that does so.
The point I'm trying to get at with my discussion of Descartes is that when science and religion really began to branch off from each other, it was more of a separation of one thing into two. Just as natural science and mathematics stemmed from philosophy, science and religion branched off for much the same reasons. They were two independent fields of study/inquiry and it was during the Enlightenment period that this point was really driven home.
I don't completely agree with the strict secularization of the sciences that we are presented with today. However, I do feel there needs to be a dividing line between the two. There are countless innovations and technologies that would have never been discovered if science was contained strictly in the theological realm.