There is absolutely nothing wrong with having a close relationship with a teacher. Teachers are very involved in your life and sometimes things just click. I think there is always something a bit uncomfortable about a close friendship with a teacher since they are the ones in power and the ones being paid in the situation. But yes this is a fine type of friendship to explore.

But--and this is a very BIG but--a friendship with a teacher should be just that: a friendship. Sexual relationships between teachers and underage students are not only illegal but also totally unethical, given the amount of power a teacher has over a student. No matter how you may feel, a teacher's age, experience and authority give that person an unhealthy advantage over you. If you keep some physical and emotional distance, a friendship will be less complicated and much more comfortable for everyone.

Exchanging Christmas cards, on the other hand, is probably just fine.