do we like someone because someone likes us?

I met my professor just yesterday who is around 90 year old. I used to be his favorite student in class. to the extent of being the envy of other students in the class.I was favorite due to my sincerity. And i also like the professor a lot. In spite of being ninety, he never forgets me, my name when i call him. I had called him after around two whole years. to my surprise, he remembers me very well. while he has long forgotten my hubby who was my classmate for the very same class.Needless to say, i also like the professor a lot and take pride in telling everyone that I was his favorite student.
It just came to my mind, that liking for a specific person, is it inter-linked? is it that we like someone, because that person likes us?
Even in school, we tend to like the subjects of the teachers whom we tend to like personally. We tend to not the like the subject of a teacher who is very rude to us, not very kind and all that, at least when we are kids. then off course we eventually understand, that every subject is important and all that.. join the rat race irrespective of whatever.
sometimes in my mind, i think, is this phenomenon only for me for everyone.. do you feel the same.?..