For some trees, water sprouts and especially suckers are normal in their life. But no matter what the plant, they will be encouraged by tissue damage or plant stresses. This is another reason why pruning with correctly sized and sharp pruning tools is so important. While the end result of even correct pruning is positive, it still damages the tree. But a smooth, clean cut done correctly is far less damaging than a ratted cut, or just being broken off.
There are a few "stop suckers" chemical treatments on the market, but I don't know how they work or even if they work, so I can't comment.
