Why can't mazda 2 idle more than 2000 rpm when starting the car?

It's normal, the idle speed is generally 700- 1000, and some cars will exceed it. At first, because it was a cold car, the oil temperature didn't come up, and the friction between various metal parts was relatively large, as was the case with all cars. As for whether your speed is too high, you should go to the 4s shop for identification.