There are two different reasons as to why you have to push in on the handle when turning the faucet off. There is no exact way to tell which of the two are causing the problem. One reason could be that the threads inside of the faucet itself are getting worn out. The only way to fix this issue is by replacing the faucet. It may also be the threads on the stem. If it is the threads on the stem then the problem can be solved by replacing the stem.
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