1. On the one hand/side, I can see why he is mad, but on the other side/hand, I can see why she was offended by his comment too.
(You can also say "I could" instead of "I can" but Americans usually say "I can" in this case.)
2. On the one side/hand, I can see why he wants to move to China--it is a beautiful country and he can learn Chinese there through immersion there--but on the other side/hand, I can also see why his girlfriend is annoyed by his decision, especially since this means they will either have to take a break from their relationship or try to maintain a long distance one.
3. I don't know what to do. On the one side/hand, I could stay here and help my dad with the camp this year. On the other side/hand, I could go to Hawaii for the summer to visit friends.