Again... the Mercury Thirteen experiment was a thing eight months before the book hit shelves.
The experiment was flawed, but it was still a thing that happened; it's reasonable to assume that Heinlein knew about it and was influenced by its (flawed) outcome.
There hadn't been much effort to bother investigating the outer limits of performance in piloting between sexes prior to the Mercury Thirteen.
Heinlein dealt in speculative fiction. in 1959, it was plausible.
It was false, but it was plausible.
Again... the Mercury Thirteen experiment was a thing eight months before the book hit shelves.
The experiment was flawed, but it was still a thing that happened; it's reasonable to assume that Heinlein knew about it and was influenced by its (flawed) outcome.
It was flawed. They started with a much more narrowly vetted initial group than the initial male candidate group.