That's one take, sure.
But look at the examples again.
Taking out the trash involves lifting something that's usually heavy, twice. So the person that's more likely to have the higher upper body strength handling it makes sense.
Mowing vs gardening, you have a similar difference; particularly looking back at pre-powered mowers. Again, the person with the advantage of muscle mass is going to have less trouble doing it.
Cooking inside vs grilling? A lot less sensible. I really think that comes down to meat and fire rather than any practical reasons.
If you also look at the division of labor for those tasks through the lens of when they became stereotypes, you might notice that trash and mowing are very much a part of suburban life compared to rural or urban. The era when that became the way things work here in the US (where the stereotypes are mostly from) was one where the wife was at home and the man out at a job. Not universally so, but close enough.
The division of mowing and trash is also split along the lines of what needs doing steadily vs what needs doing irregularly, but takes more time to do at once. In a lifestyle where one partner has less day time available at home, them handling tasks on weekends and/or at end of day makes more sense as well.
The whole post war era here in the US shifted home dynamics into that kind of weird dichotomy. Not that the idea of women's work vs men's wasn't a thing everywhere, or that it only existed during that time. It's about this type of home tasks being split up by the standards of the lifestyle people thought they should have.
There's also the mess factor, and a shit ton of people born before the eighties or so and after maybe 1900-ish definitely had a concept that women shouldn't have to get dirty on a regular basis. Gardening in the suburban sense is a vastly different one than in the rural sense. In a suburban area, you're either talking flowers and decorative plants, or a small vegetable/"victory" garden. Neither of which is as messy or as large as an acre of crops to handle.
Mowing is a high sweat, messy job. Grilling compared to indoors cooking is a tad messier by virtue of the soot and ash.
I kid you not, doing home health back when the generation before the baby boom was solidly into old age, the more suburban a family was, the more likely they were to have the assumption that women shouldn't have to deal with the more physical, messier home maintenance jobs. Baby boomers carried it over for sure, but for them or was often that they grew up with that paradigm and didn't question it until later. I had way less gen-x patients that had a sustained home paradigm, so there's less direct observation for that, and next to zero for millennials.
I'm not saying it was right. I'm not judging it one way or another, not really; people can have whatever home arrangements they want, ain't none of my business. I'm just saying that it isn't as single facet as the screen shot tries to make it. It is/was a product of a full cultural shift and it wasn't as arbitrary as that makes it out to be.
