[special case is] mathematical mumbo-jumbo.

It's a standard concept in high school math, at last when I went to school.

Arguing that everyone should be punished and penalized for having relationships that offend you

They don't offend me in the least in principle -- I am attracted to girls, you know. Even 3-year-olds. But my judgment about how girls (at least 99% of them) operate and think and develop leads me to oppose it for their sake.

... and "polite" society when there is no demonstrable harm in evidence is not compassionate

There's a law against it, right? Everyone knows the law, right? Even if the law is unjust I don't see any reason for outrage on behalf of those who break it. I think the social security tax on wages is unfair and should be replaced by a slightly higher rate on the progressive income tax. Will I be outraged at legal penalties leveled against those who (somehow) manage to avoid paying it? No, I work to change the law. Until then, it's understood you've got to follow it.

Underlying a lot of these disagreements is the frequency distribution -- how many girls actually want these relationships? In this little pond you mostly say it's substantial, everywhere else in society people think it's extremely low.

I've raised this before, but I'm going to do it again, with commentary: Some adults feel a profound desire to have a limb removed to make themselves in line with their self-image (it's in line with our support of trans people transitioning). Society lets them do this. Now, presumably some children would also like this -- they feel profoundly wrong with that extra leg when they only want one. Yet society will not permit this. What an outrage! Denying children the right to self-determination! The main reason I oppose this is that I think the baseline rate of genuine desire for this is extremely low, and the chance that something else is involved (depression, a desire to be a rebel, etc.) in such a request is much higher. In the past, the GC reaction has been, "How dare you compare a desire for limb removal with consensual sex!" That's an example of an appeal to emotion rather than reasoning if anything is (what I get unfairly accused of). So maybe you're profoundly prejudiced against those who want a limb removed and it's showing. If not, then why? What makes it relevant in my mind is the role of extremely low probability as trumping self-determination as a principle that overrides everything else.

I can achieve a better understanding with anyone who concedes this point and we know our difference has to do with that estimation of how often girls really do badly want sex with older men.

As for perfectibility, "people naturally gravitate towards tasks that they have a natural aptitude for" may work for many, but thinking it will work for everyone (or almost everyone) requires a rosy view of human nature. Experiments with collective agriculture have generally been miserable failures. Benefits are shared equally between those who work hard and those who don't, and as a result few people work hard and it collapses.