I think you are misunderstanding my main idea.
I think that is one of the problems. When I read the essay, I felt that it is on your love for teaching. However, when you brought up that point about learning with students, I became unsure. So right now your essay has two distinct themes which are not properly interlinked.
Anyway, I think it would be great if you can incorporate the obstinate learning thing with the main theme.
^^It's a personal opinion though.
Is "a love for teaching" considered a personality?
Personality is a broad term. According to the prompt, you're supposed to talk about an attribute of your personality, and "love for teaching" should qualify as an attribute.
I've read the other essay. I think it suffers from the same problem. However, since that one is a bit wordier, you can get away with it. The anecdote you are referring to is on a completely different topic -- at least it seems to me that way. You can write an entire essay on "obstinate learning."