IMO, "come to" means that, after a while, the conversation leads them to realize thet both are teachers.
If omitted, the meaning might be only slightly different, in the sense that, for instance, at a certain point one of the speakers asks the other something like: "So tell me, Hubert (random name), what so you do for a living?".
Hubert answers "I'm a teacher at Fail School (again, random name). How about you, Egbert?", and Egbert answers "I teach at Cognate School". Now they know both are teachers, but the way of learing that is different from "coming to know it".