I found that when I am depressed the last thing I want to do is get out of the house. Thankfully I have friends and family that push me to get out, although for the past week I've been really down to the point of illness and haven't found a good enough reason to leave.
I understand how you feel. I started a stupid fight with my boyfriend because I felt angry, and now I just feel numb.
I think the best thing to do is to tell your dad how you feel, and that you're down and don't mean to push him away. I think he's trying to help, but maybe that isn't what you need is his help. Depression can be really hard to understand for someone who doesn't have it, and even for those who do. Sometimes I don't understand why I feel the way I do - I just do.

Let your dad know that you love him, but you are just going through a tough time. You don't mean to push him away; you just don't know how to feel anything right now, and even though he is trying to help that there is no quick fix for your feelings. I bet he's just trying to make his little girl smile again, and it frustrates you because you feel he doesn't get it - and he probably doesn't. But don't get angry. Just let him know you love him and appreciate his efforts and ask for him to patient.
You'll get better. Are you on medication of any kind? It might help with your feelings...