Both statements - "sexism does not exist" and "sexism is everywhere" are equally extreme. By saying the former you deny the obvious. By saying the latter you effectively claim that every single person is sexist, which is a bit unfair.

Except that the extremeness of the statement is subjectively based on your own outlook. And there is an implicit value judgement in making that decision about what you consider "extreme". Arguably all people are sexist, but not in a particularly problamatic or socially unacceptable way. It is human nature to notice gender after all. And applying such logical rules to something so nuanced and subjective is flawed, and will unavoidably lead to an argument over semantics.

> I could just as easily say the opposite statement (that sexisim is minimal) and suggest that it requires extraordinary evidence to prove that

You could, and it does. But it's it matter of opinion/semantics that this is "the opposite statement".

In context, a specific claim is a specific claim, whichever way it goes. The "opposite" in another sense, is to make no claim, and therefor stick to the default position of allowing for either possibility without knowing which (agnostic position?). There is absolutely nothing wrong with that position, and it requires no additional information, as opposed to "less formal information".

Now, if you claim we need to adopt a specific position, and do so with little information, i.e. without the time/money to do so then you'd have to justify that - i.e why isn't it strongly desired, yet still apparently important, to hold a position on the topic?