There are many things to talk about that bridge the age gap. Students may be surprised to learn teachers were equally enthralled by the musical stars of their day. Tales of struggling with homework and final examinations humanizes a teacher, and makes students feel like he or she is "one of them." Anything that narrows the perception gap where students see teachers as out of touch with their world promotes friendship.
Befriending students is not a problem.
However, given the fact we are only human, it is possible to become friendlier with some students than others. Indeed, it is possible that attempts to befriend students may lead to the discovery that some are simply hard to like at all! And those positive and negative preferences can begin to influence classroom behavior on the part of both teacher and student.
Fairness is critical in teaching and if your behavior towards certain students with whom you are especially friendly even hints at favored treatment in any way, the other students will sense the favoritism and react accordingly.
The fairness principle applies to all educational environments - elementary education, graduate education, and industrial education. If the trainer is on a company sponsored athletic team with a few participants and appears partial to them in the class setting, that can cause problems.
This presents a real ethical dilemma for many modern teachers. Ethics is about principles of right and wrong. Certainly it is not wrong to befriend students and in fact can be beneficial. But how far can one go before friendship extends to favoritism in the class?