That's a good, relevant, moving quote. But the end of it is the sort of eloquent and persuasive bullshit that Heinlein was so adept at slinging. This is the voice of a 54-year-old man telling himself that growing old doesn't matter to us guys -- because men "were never meant to be admired." Meant? By whom? God? Natural selection?
If we're talking about evolution, the truth is just the reverse. In most species, the males (the ones with the innumerable, tiny, cheap gametes) sing, dance, display, and strut their stuff in hopes of being admired and chosen by the drab, non-singing females (the ones with the few, big, valuable gametes). Both human sexes display, because the males help feed the babies. But -- males never meant to be admired? Horse apples (to quote Rainbow Dash). If men were indifferent to getting old and un-pretty, President Trump wouldn't be combing his ear hairs over the top of his head and dyeing them yellow.
Incidentally, the first time I ever saw that youth-restoring gimmick, the skin that was being pulled back was on the face of a man -- Robin Williams in Hook