Well, normally, Jedi Masters choose their own Padawans. And usually not until they're much older. Anakin had only been knighted for about six months at that point-- he'd only just turned nineteen. If I had to hazard a guess, I'd say he probably didn't feel ready to take on the responsibility of looking after a fourteen year old on the battlefield.

But the Clone Wars changed all our usual traditions. The Order didn't have time to wait around for Masters to pick a new crop of apprentices at their own pace-- we were stretched too thin. They just had to start assigning people, ready or not, to get every able-bodied person onto the field that they could.