Latin soup, comin’ at you like a food fight in an elementary school without recess…

The university system in the modern West was born in the late 12th/early 13th century. Universities evolved out of what we call “cathedral schools,” primarily as a place to train the preachers and teachers the Church suddenly realized it would need if it wanted to keep a newly-interested laity loyal to its doctrine instead of following heretics. Keep in mind that the primary function of medieval universities was to churn out the equivalent of an MDiv: preachers.

Very early on, the teachers were called magister or doctor or both, depending mostly on where you were in Europe. Magister comes from the title used in the universities’ predecessor, cathedral schools, with specific reference to the person who ran the thing. Doctor (Latin for “teacher”) comes out of the early Church: the word used for a great theologian, which is to say, a great teacher.

Since the universities had to train their teachers, gradually they became a formal rank that was tested and bestowed after fulfilling certain requirements of study. The ultimate prize, if you wanted to "go career," was being permitted to advance beyond the basics to the specialized disciplines of law, theology or medicine. That idea of more advanced studies is where we get the formal doctorate today. And, incidentally, why medical doctors are technically called "teacher." I've not read a coherent account of how schools universally adopted both master and doctor with near-universal agreement on their hierarchy, so if anyone can fill that in, I'd love to read it!

Bachelor is a little more complex. The word universitas in the 12th/13th century still referred to a legal entity, a group of people—the archetype is a trade guild. The universitas of a studium generale (place of general studies) was its teachers and students. The label gave them the legal rights to control their profession: to determine what was taught, how to advance through the ranks, what made someone qualified to practice that profession. The profession in this case being preaching, the creation of Christians instead of Cathars.

Baccalarius (which will become baccalaurius, as in “baccalaureate degree”) seems to derive from a term used in contemporary universitates for the apprentices. That’s what our university bachelors were. Students all began with a liberal arts curriculum, finished that, and then spent some time learning what they’d be preaching and how to go about that. It was hands-on learning: they were required to teach the newer students while they continued their own studies. They were apprentices in a guild—baccalarii in a universitas.

And thus, the T.A. was born.