Empathy supports relationships in other ways as well, such as by helping you understand another person's inner workings.
Being comfortable with closeness supports empathy and compassion.
Nonetheless, humanity's evolutionary heritage (in which the greatest threats usually came from other people), combined with person real life experiences (especially childhood ones), can make an individual uncomfortable with closeness.
Ways to increase comfort with closeness include focusing on your internal experience instead of on the other person, paying attention to awareness itself, using imagery, and being mindful of your inner world.
Buddha's Brain - Hanson