By the "gear arm" I assume you mean that part of the rear derailer that the chain zig-zags through. This arm moves in two ways. It moves in and out (toward the wheel and away) as you move the shift lever - which is how it changes gears, by moving the chain onto different sprockets (gears). It also moves forward and back (toward the front and back of the bike) under spring pressure. This forward and back motion is necessary to take up the slack in the chain when you are using the smaller sprockets (the smaller the sprocket, the "higher" the gear). When the wheel has been removed, this arm moves forward (under spring pressure) as far as it can to take up all of the slack in the chain. All you have to do is grasp this lever and pull it toward the back of the bike, allowing the lever and the chain to pass behind the sprockets (gears) as you pull the wheel back into it's position. You can safely pull this arm forward and back at any time without doing any damage. One more tip-- I find it a little easier if you first put the shift lever in a "middle" gear position. Then when you pull the wheel into place, you should aim to put the chain on a middle sprocket. You don't have to hit the exact correct sprocket as you can simply lift the rear wheel and turn the pedals forward (after installing the wheel) and the chain will move to the correct sprocket corresponding to the setting on the shift lever.
Good luck! Please vote if you found this helpful. Al K