graduate programs. There are some, sure, but they are more rare, especially compared with other universities. The Church sees BYU as a place where undergrads learn to combine spiritual and secular learning, and with that foundation go into the other great universities of the world for grad school. Hopefully having picked up a spouse along the way.
You might ask, why does BYU have a law school, which has a grad program only? I don't know the official answer, but I bet the Church in part wanted a way to tap into readily available legal expertise when needed. I'm not sure the Church feels it needs its own dentists at this time.