Hogshead joined "TMZ Live" on Tuesday ... and addressed statements Thomas made earlier in the day when she joined Good Morning America for her first interview, telling Juju Chang ... "Trans women are not a threat to women's sport."

But, Nancy, who also runs a female advocacy organization called Champion Women, told Harvey and Charles that Lia is just wrong.

"After somebody has been through male puberty, you cannot roll that back. So, it isn't fair," the former Olympian said, citing several experts.

"We're hoping that we can get sports governing bodies and legislatures and others to care more about fairness than any other conclusion."

It's not that Nancy isn't supportive of Lia Thomas -- she says she is -- everywhere except the swimming pool.

"I affirm who [Lia] wants to be for all of her life. Whether it's employment, the classroom, or anyplace else. But when it comes to sports, sports is not based on identity. It is based on biology. That is why we have the women's sports category."

FYI, the UPenn swimmer, an NCAA champ in the 500m freestyle event, is done with college athletics after recently graduating. However, Lia isn't done competing ... she's made it clear she wishes to compete in the Summer Olympics in 2024.

And, Hogshead believes the future of women's sports is literally on the line.

"If sport is not based on sex segregation, and if gender identity equals sex discrimination, we might lose the right as woman athletes to be able to have separate sex sports."

That's something Nancy is intent on preventing from happening.

"I am not going to allow this generation of women to have to be gracious losers to somebody that has a biological advantage that you can't train for, you can't eat better, you can't find better coaching," Hogshead said.