If this was a really close friend that was only laughing at the irony that folks like us would choose teaching as a profession, that would be ok. Let's be honest, it's kind of funny and brave at the same time. But when you added that she has truly insulted your intelligence in the past, I question how much she respects you. As others have noted, friends, particularly if they're adults, should never make fun of you for that. For what it's worth, my twin brother, who also stutters, even a bit worse than me, learned German on his own, went to German university, and now teaches history in both german and english there. He said at times it's a struggle but his students love him and he gets positive reviews from the Principal. You can do it, just hang in there.