All they need do is make an accusation against any man, and his ship is sunk even if he never laid so much as a finger on her under any circumstances, just in case there is the remotest possibility that her accusation might be true.

Completely false and unsupported by anything I've ever said. It's hard to believe you make this accusation in good faith, unless your mental abilities are slipping.

A girl must prove that sexual activity took place, and meet the usual standard of "reasonable doubt" for such an accusation to stick. It's only when it pertains to whether she consented to this activity that she need not prove anything.

I'll now expand on how girls are a "special case" as I intended it. Anyone can make false accusations. Lately it's women's accusations that have been in the news, many of them true, a few of them false. And we are right to want very few innocent people punished even if it means many guilty people go unpunished. Suppose you lower the age of consent to 12 (as a rough approximation). Now girls who say they consented will be believed. Those who say they didn't will have to meet the same standards as adult women. In fact, as I think about it now, we've actually opened up a new realm of false accusations that didn't exist before. Today, saying that she did not consent has no legal ramifications because the man is guilty anyway. With a lower age of consent, you introduce the possibility of false accusations that do have legal consequences.

As noted elsewhere, your objection fundamentally rests on the idea the quite a few girls do want and consent to these relationships with older men.