It feels awkward because when you throw the left hand the right shoulder moves backwards, pulling your left forwards. Once the shot it thrown the motion of bringing the left shoulder back to your normal stance makes it a good time to throw a right hand because of the forward motion you get on the right shoulder.

You need to practice throwing the jab and returning your left shoulder into the position it would be in if you where leading off with the left hook.

One way of thinking of it is to throw your jab, pretend to throw a right hook (but don't :P) and by that I meen drive the right shoulder backwards so that it pulls the left shoulder backwards. Its almost like a lever.

To be honest its not that hard a shot any way, I good points scorer because generally if you get guys coming at you throwing: left, right, left, right - after he's thrown his left hand he's got you in the habit of waiting for a right hand and defending that side of your body.

But because you have to reposition your shoulder to throw the left hook hard its easier to see coming then if you throw it softer and faster to score your points or open up for something bigger.

if you threw a left hand your on a prime position to throw a fast fully thrown right with all your weight in it, harder to see coming but more predictable (you'll find in boxing alot of the punches you don't really see coming, you just learn to read what your opponent is going to do, if I tryed slipping a shot by waiting till I saw the glove move from the other guys chin I'd be brain damaged by now :P)