I'm a SAHM and just can't get annoyed about this. I was actually chatting to FIL the other day about why we get 15 free hours recently instead of 30 free hours, and I said it's because I don't 'need' the childcare for 30 hours a week. He said 'but it's not as if you're not working is it?' which took me by surprise to be honest, I don't feel as though I do 'work', I suppose because I view work as not only paid employment, but having to work to someone else's schedule, having deadlines etc. There is no way my life is harder than that of a working parent, a working parent still does all the things I do but fits other responsibilities into the same amount of time.
Agree with a PP that it's impossible to make comparisons anyway. Some working parents might have a full time nanny/cleaner/housekeeper and a SAHM may have no household help. Equally a working parent might be just about making ends meet and spending every spare evening trying to keep the house together, and a SAHM might have a cleaner plus some childcare during the week.
Even between me and a close friend, we are both SAHMs but completely different set ups. She has a DH who is around a lot, always around to do the morning and evening routine, home at weekends etc, shares school runs but cash flow is poor so they aren't able to pay for any preschool before the free hours, a cleaner etc and have to be frugal with the food shop.
My DH works very long hours, often seven days a week, yesterday worked 7am-9pm and that isn't unusual, but we have more cash flow so I'm able to send my children to preschool since they turned two, we have a cleaner and I cut corners with takeaways/pre prepared food etc.
I think really we should just be striving for respect and empathy for all parents in all scenarios, all people in all scenarios even. Everyone has things that are difficult in their lives and things that are easier than someone else's. Bickering over phrases isn't really very helpful.