Why do they carry the ball by the middle in rugby?

You can carry it anyway that you see fit or are comfortable with.

No, there is no rule - the nature of the game makes tucking the ball away less practical.

Other than plays where the QB pitches to a running back, it is rare for a ball carrier to attempt to pass the ball to a teammate. In rugby, the ball carrier is always aware of teammates around him and is looking for an opportunity to unload the ball. This can be done to either side, so it is important that keep the ball in available.

When an American football ball carrier is tackled, he needs to hold on tight to the ball to avoid a fumble. In rugby, the ball carrier MUST release the ball when tackled, if he doesn't his team gives up a penalty. So again, if the ball is tucked in tight at the elbow, it can be much more difficult to release the ball.

Because the rugby ball is much bigger than your American football, point is really in rugby you pass the ball down the line whilst running towards the end and take advantage of any openings. The other thing is because of the size of that ball I punch it out of your elbow faster than you think mate. Even your American football hold it in the elbow and any rugby players could rip it out from you, hold it in with all your might fighting off anyone who comes close is much more safe. Sorry what I meant from the passing the balk thing it's much easier to pass from the middle, you can only pass backwards so if you had it in your elbow you have to put much more effort into passing than just swinging it whichever way you wanna pass too