My BF of 1 year hates to show emotion in public. When ever we go out I reach to hold him or kiss him and he pulls away or does not move at all. This makes me feel inferior and I have doubts about his love for me and if I should continue with the relatioship.

Some people just do not like to show affection in public. This does not mean that they love you less, it simply means that they prefer to keep their lovelife private.

I would recommend that you talk to him about your concerns. Only he can tell you why he feels this way.

Why is being emotional in public so important to you. I prefer my privacy, maybe he does too. I do not think it has anything to do with how much he likes you
You didn't mention your age but could this be an " I want everyone to see how much he likes me.

Neither my husband or I are into PDAs or public displays of affection. I don't need to have him all over me to feel secure in his love.