Regardless of sex, if one parent has had the luxury of staying at home, most of the chores done, including dog walking. If I was the earning partner, I would feel inclined to say work isn't optional, really sorry but this course is merely a hobby, ask for notes, see if the course leader can send you as much as possible to catch up.
Ok if I could work from home I would. But there might be stuff I need access to in the office, so it doesn't matter if I've no meetings, I might have planned to call on a colleague, or monitor a situation.
So whilst it seems unfair, the parent at home, male or female, as there's men who have such circumstances, then surely you'd try and accommodate the at home partner as much as you could, but you would also think well DC is 15, they've not been ill in 2 years, so in the week you have your hobbies, you have friends you meet up with, male or female, life is pretty easy. Only real task is cooking dinner, I'm guessing you'd have a dish washer or leave pots for cleaner.
I can see his point of view as he must be a high earner, with being a high earner, usually there's a lot more responsibility. At the age of 13/14 onwards, I think you would deviate from SAHP to HouseWife/Husband. Or Lady/Gentleman of leisure. As you may have to prompt DC to get up, get to school, then on return chivvy them to do homework and sort out school uniform from PE kit for another person to wash/iron. It's not like having a 6 year old where the child isn't as independent.
When the child reaches Sixth Form, University, of course you're there in case of emergency, but I suspect the SAHP wouldn't suddenly be seeking work after 16 years as a SAHP.
I don't see it as a sex orientated issue, as I've worked with DH being at home. So it does work both ways.
I think you have to be clutching at straws to say the working partner has it easier, when literally almost everything is catered for, bar cooking. I agree it's a shame that the SAHP would miss out on a pre-planned activity. For me at this age they'd have to be considerably ill to warrant hand holding 24/7, unless they had other issues.
An unpopular opinion, but I can see both sides.