@prepschool2021, I get this, as a parent of a very math-y white boy. Though I think it is about boy jock culture generally, not necessarily just white boys. There is a lot of pressure of American boys to fit a particular mold.
Fwiw, there is a great book on it called Masterminds and Wingmen. My kid definitely experienced it in middle school, and it was one of the reasons he went the bs route.
It exists at bs too, but I think it is much easier for a boy to break the mold (embrace being a serious student without jeopardizing social status) in bs.
Not sure if it is something admissions offices think or talk about, though. I have always been curious about that. It is a delicate topic and one can’t lose sight of the historical privilege white boys have had in the prep school world (which in itself is the ground zero of privilege in many people’s eyes). It is complicated and it raises a lot of Big Questions.
But back to your issue - your academics sound great on paper, with or without the SSAT. If your scores are good, they will serve to validate your aptitude. But don’t confuse that with showing “what you learned”. The SSAT is about something different than what you learned in school.