Vladimir Khorikov argues that you should not unit test private methods:
When your tests start to know too much about the internals of the system under test (SUT), that leads to false positives during refactoring. Which means they won’t act as a safety net anymore and instead will impede your refactoring efforts because of the necessity to refactor them along with the implementation details they are bound to. Basically, they will stop fulfilling their main objective: providing you with the confidence in code correctness.
When it comes to unit testing, you need to follow this one rule: test only the public API of the SUT, don’t expose its implementation details in order to enable unit testing. Your tests should use the SUT the same way its regular clients do, don’t give them any special privileges. Here you can read more about what an implementation detail is and how it is different from public API: link.
In the database world, this is one reason why I like using stored procedures: they give the equivalent of a public API for database code, so you can write tests for them.