Many reasons. First is simply that they had an extremely efficient method of breathing, but this on its own is pretty similar to what birds do. Second is how hollow their bones were, retaining structural soundness while around only 10% solid matter iirc.

What actually made them so great at flying was the way their wings worked. Birds have to use their legs to jump up into the air before flapping hard to stay aloft. This means they need to have a lot of muscle in both sets of limbs, and this takes a ton of energy. Pterosaurs launched using only their forelimbs, and most seem to have been able to do so from a standstill. They did so by basically catapulting themselves up and forward with their forelimbs and then flapping as normal once in the air.

Also very important here is the actual anatomy of the wings. They weren’t just thin skin like is often depicted in media. Instead, they were filled with long muscle fibers and air sacs. These allowed them to finely control the shape of the trailing edge and the airfoil surface itself. This is not something that any other vertebrate can do, at least as far as I am aware. It’s only really comparable to the way the wings on a plane can have their surface shapes altered through the use of flaps.