Stop getting punched by punching back

Well, last night's boxing class didn't exactly boost my confidence. It's not like I got my ass handed to me, we didn't even do light sparring, it was just one of those classes that reminded me how little I've learned in the three months of taking classes. My punches felt weak. My footwork was ... I can't even find a word for it. I'll just say that at times I was stepping forward with my rear foot. My rear foot! And my partner wasn't any help either. Not because he didn't know what he was doing, quite the opposite. I was partnered with a guy who shall remain nameless (he has a Russian accent) and is way better than I am. Running through the drills with him made me feel like I was a little child who just stumbled out of his sandbox and into boxing class.

This illustration from Wikipedia
 demonstrates the counter punch
without blocking first.
Boxer A's left jab is countered with
 Boxer B throwing a right straight
 punch to the head.

We practiced countering for the entire class. Partner throws a left jab, I block it with my right arm and counter with a straight right; partner throws a straight right, I block with my left and counter with a left hook. It feels incredibly weird to counter with the same hand I'm blocking with, but it makes boxing sense. When you block a punch with your right arm, you have shifted your weight to your right leg, and we all know you can only punch from the side of your body that your weight is on. While this makes boxing sense it does not feel natural at all. In my mind, when I block a punch I want to keep that hand covering my face. My thinking goes like this: Holy crap, I blocked his punch. I can't believe that worked. Well, that hand did its job, I'm gonna keep it there where it's protecting my face. Wrong, wrong, wrong. When your opponent punches, it is a great time for you to punch back. Problem is, I want to counterpunch with my non-blocking hand.

Another issue I have with the counterpunch is a mindset problem, one I touched on when I first started the boxing classes. I am not attack oriented. I'm defense oriented. So when I block a punch, I fall into the trap of thinking that I can just keep on blocking punches, as if my opponent will grow weary of hitting me and give up. But blocking punches isn't going to win the fight. Blocking is only something you do when absolutely necessary and when you are not punching. The only way to stop getting punched is to punch back. Since I am defensive minded, the counterpunch should become a move I like because it relies on my opponent committing and me exploiting his opening.