I assume the answer is largely because why are you catching it if you can’t handle it? Why not let whomever can handle it (or whomever is left with no choice but to handle it) log it, if they feel that it is log-worthy?
If you catch it and log it and rethrow it, then there’s no way for the upstream code to know that you’ve already logged the exception, and so the same exception might get logged twice. Or worse, if all the upstream code follows this same pattern, the exception might be logged an arbitrary number of times, once for each level in the code that decides to catch it, log it, and then throw it again.
Also some might argue that since throwing and catching exceptions are relatively costly operations, all this catching and rethrowing isn’t helping your runtime performance. Nor is it helping your code in terms of conciseness or maintainability.