Well, gender may have something to do with it; but that may in fact be a
result rather than a cause.  I'd suggest the following alternative.  Museums
have a connotation of being collections of old stuff.  "museum piece" is
synonymous with "obsolete".  We live in the midst of a commercial culture
that thrives on convincing the public that the old is worthless, that they
need to buy the newest stuff.  We also live in the midst of an industrial/
technological culture that in many areas does render old stuff worthless.
(Would you want a fifteen year old computer sitting on your desk?)

If there is a difference with respect to Europe, it might be the pervasiveness
of commercial television in the U.S. hammering in the messages that you must
acquire new stuff constantly.  Or it might be the history, Europe for a long
time having been ruled by kings who found it in their own interest to be the
descendants of a long line of heroic figures, and rightful heirs of the glories
of the past.  Perhaps there is something genetic involved, the New World
having been settled by people who were willing to leave the Old World behind
and move into places that had no (to them) history, leaving the Old World to
those who were not so willing to leave history behind them.

I think of another gender factor (this is coming from one who loves museums
but isn't involved in them professionally) is the extent to which the titular
"head" of a museum, like the president of a college, is supposed to be more
of a fund-raiser than an administrator.  So a fund-raiser has to go out and
rub elbows with the people who have the money; and those are the business
leaders who are predominantly men.  Perhaps it is perceived, rightly or
wrongly, that on the average men are more effective at getting money out of
other men, and that is the main thing that matters.