Chris W writes:

How is not wanting to embarrass yourself in front of your significant
other, a "19th-century mindset"?

Wanting to do things "among the girls" would be a 19th-century
mindset.

In any case, her reason for refusing is a matter of total speculation.
It could have been anything. Why not just accept it and move on,
without casting aspersions upon her simply because she is different?

Not wanting to look stupid in front of other people seems
to be a pretty timeless concept to me.

My own guess is that she simply wasn't interested in flying a plane.

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