So I have two goldfish and one of them keeps pushing the other one by its tail. It stopped now but the fish stays at the bottom.
It is not very common for a goldfish to bully another, but it may depend on how big the tank is. If the tank is under 30-40 gallons, the fish can become very territorial, usually the bigger fish is the dominant one in this case.
If the size is ideal for them, one fish is likely being bullied because it may be a bit newer then the other. Although in some cases, the goldfish that is being bullied is sick or infected, causing the other fish to think the sick fish is lesser than them.
The solution for this is to separate the goldfish into different tanks each 15-20 gallons or more. You can search google for more suggestions to what they may be doing, the possibilities I wrote are just some more common reasons for a goldfish to be bullied.
The fish could just be playing, but even then it would be weird for one fish to not be eating if they were just playing.