If this level of chivarly were hardwired into the human race, then we
would expect to find it in many different cultures. Do you think it existed in India? How about the Middle East? Or Imperial Japan? Or China?
What we're talking about on this thread was a relatively short-lived
practice confined almost entirely to the English speaking world. And as Elinder and Erixson document in the paper Gender, social norms, and survival in maritime disasters, it was relatively rare even in that sphere. We know of only three instances where it actually happened. We know of at least a dozen others where it did not.
I think a great many women would disagree with you on the question of courage. Here for example, is brief snippet from a German love song: (Translation is mine)
"If we were on the Titanic
No tomorrow and no more land to see
Then we would know the meaning of true love
If we were on the Titanic
Then I would go down with you
While the string orchestra played its last song
Even if it costs me my life, that's completely of no account
Because so great a love won't happen again."