But I'd hope that for many parents, having a day with neither work nor childcare might be an opportunity, might be appreciated, might be a time, finally, where you can rediscover & do some you.
Daycare is great for the kid. The teachers can provide much more attention and direction on things that I simply can’t, and he really gets a leg up on social skills being with other kids, not just mom and dad. Spending long stretches at home with just mom and dad (and given COVID, without many play dates), he tends to become a bit wild…three day weekends or week offs aren’t just harder in a linear manner.
I feel even worse for layering on more here, but I think, ultimately, one of the best things a parent can give their child is a sense of personhood. It's one of the slowest, least clear lessons, and the impact seems slow to naught, but having hobbies, doing things, having your own interests as a parent is setting a model of being interested in the world: of engaging yourself & demonstrating control & direction & volition. Parents- in living- to demonstrate what a self is.
That idea- of a world where we can visibly see others who are motivated, have intrinsic motivations desires and pursuits- beyond subsistence & survival- I think that's a keystone factor in the world, in what has made humanity enduring & interesting & capable. I worry after it, significantly. And I want, very much, for parents to have time & permission, for their self to continue to mature & engage, and to not just have to always be engaged, always be tending or working.
I have plenty of time & I spend a lot of it somewhat-inertly, so I can't expect too much from 1 day a week where there might be no work & not constant family. But I do have lots of pursuits, and they do help me shape myself, help me grow & see myself over time. I want very much everyone to have some option, some time to explore on this earth, engaging, not just being engaged.
There are people who have the opposite experience and people who feel ok with both.
This idea that parents should uniquely and equally be caretaker for their kids is absolutely against biological reality for a lot of people; I'm happy to be around my kids for a limited amount of time (and the less they're toddlers the more I can spend with them without going insane) but my main contribution is providing them food, shelter and protection.
My mandated paternity leaves, while being economically advantageous, were an absolute nightmare.
For me, I just bring a package of crackers, some water, then go out in the streets with my kids, visiting nearby playgrounds or lots with trees. They'll then start playing, perhaps needing a little help getting started, and my involvement is mostly coming up with a plan for where to go next, and watching out for signs of exhaustion. So most of the time, I'm actually not active.
I also enjoy having limited help with say cooking or cleaning, but yeah, that's exhausting, because you need to multitask and both do the job and monitor their state and the job they are doing.
In countries where men have mandatory paternity leaves that are significant this imbalance is greatly reduced.
You could actually spend time on thinking what you could do with your kids.
Why did you get kids in the first place?
But even if what you say is true I'd still say he doesn't want to be a parent. You don't pick and choose with parenthood.