Why don't passenger planes move back by their own means before taxiing?
I’m not exactly sure, but it sounds like you’re asking why planes need a tug on pushback. Some jet and prop planes such as the 727 and MD-80 can perform a power back where they start at the gate and use reverse thrust to exit it. This procedure was more common in the 70s and 80s but seems to have died out in the 2000s. According to wikipedia the practice was stopped to save fuel. Additionally, there was a high risk of foreign object debris entering the engines from the ramps. Thus, the procedure was even less common on low engine aircraft such as the 737. The C-17 performs powerbacks still for the armed forces, so size is not a limiting factor. 

You can check out a video here of an MD-80 powerback.