Given the responses to this thread, I'm wondering if there isn't a correlation between the relationship one has with his/her father and social anxiety. My parents were divorced when I was very young and I only saw my dad every other weekend until I was 14. When I was 14, my mom committed suicide and I went to live with my father.
Even though we talk several times a week, we've never really had a really meaningful discussion. Honestly, I really don't know that much about who he is and vice versa. Neither of us share our feelings. I'd like to have deeper conversations with him, but social anxiety holds me back.
As for Father's Day, I'll probably get him a card and some gift (I'm not sure what yet).