You are right that the issue is who will do a better job of defending the national security interests of the United States, and we can disagree over that. So why is your side bringing up baby sitting prowess as a criteria?

It reveals a certain worldview about the parties, and what they think the job of the President - and the U.S. government - generally is.

This isn't a new dynamic. I don't remember when I fist started hearing it, but back in the day you would hear politicos refer to the Democrat/Republican choice as between the "Mommy Party" and the "Daddy Party." The Democrats were characterized as viewing government as providing nurturing and kindness, while the GOP thought the government's role was more protecting against threats and maintaining order and dispensing justice. What can government help you with, versus what can government protect you from. Traits that were, in the gendered language and roles of the day, mapped onto mothers and fathers roles in the household.

Trump's pitch as a candidate is that it's a coarse world filled with bastards, that a lot of those bastards are not just foreign enemies but domestic elites that want to take advantage of "us," and that it takes a hardened and coarse son-of-a-bitch to put all those bastards in their place. That's why, I think, the message that Harris was sending earlier was so effective - it framed Trump as dumb and weird and goofy, which is the opposite of what he wanted to spin.

Pointing out that Trump isn't fit for maternal-coded jobs is not the opposite of what he wants to sell. It's consistent with what he wants to sell. He wants to be perceived as the guy who's fearless and brave enough to say whatever he wants regardless of what other people think, who'll say impolite truths that aren't necessarily fit for the nursery room. He wants people to think he's Nick Fury, not Captain America.