Working At A Hospital...

I want to work in the hospital since I'm almost done with school to be a phlebotomist.. my boyfriend told me I can't because he thinks everyone that works in the hospital sleeps with each other, I'll meet a doctor, cheat on him or have guys hit on me... I told him I'm going there to WORK. We also have no previous trust issues so this kinda irks me... opinions? How do I talk to him about this?