It's not a handwave - the article doesn't offer anything to handwave away. The article says that she was offered specifically gendered criticism, then quotes generic criticism.

I'm sure being a woman counted against her, bit if the article is going to put up a quote as evidence of sexism then it shouldn't be a passage that can be realistically adapted to any politician ever. If the article had a passage that says "we can't let this woman be king, she can't even own property!" that would be different. But the quote in the article doesn't sound ludicrous when applied to a man. It sounds like something that is routinely said of men in positions of power.

It could even keep the superficial gendering if you wanted it to, there is a lot of argument that men in positions of power should be exhibiting positive masculine bearing (stoicism, accountability, honour, etc, etc) that politicians routinely fail at to great public outcry.