On the contrary, I agree with @AnotherForumUser Women are always railroaded into childcare, and care for the elderly, it's never men. Well, very rarely. Whenever either of our DC needed a parent, (when they were little,) the school/the childminder ALWAYS called me. It was always me who had to leave work and then had to make up my hours later on, or had to use holiday leave. DH was never contacted. Pretty much the same for everyone I know.
You will never (well, very very rarely!) see a man stepping up when it comes to care duties, (or being asked to do it,) when there is a woman who can be asked. You crack on with your 'empathy' and 'kindness' Women are starting to see the light now, and refusing to be treated like handmaidens, whilst the men do largely naff-all. If your dad enjoys looking after your children far more than your mum then good for him!!! He is as rare as hens teeth though.
Nothing horrible, selfish, or soulless, about refusing to be treated like a dogsbody and saying NO. Men have absolutely no problem whatsoever with saying no.
Some years ago my DH's dad died, and his mum was starting to hint about moving in with us. We had a 3 bed house and our 2 DC had a bedroom each and we had the third bedroom, and DH wanted her to move in and let the DC share a bedroom. I refused point blank. He worked full time, shift work, and I worked part time. (Did everything in the house, all the chores, life admin, domestic shit etc, and 90% of the childcare, so probably worked more hours than DH.) I refused because I KNEW I would be the one looking after his mother and waiting on her hand and foot. He said 'she's getting lonely though without my dad.' I said 'well bloody move in with her then!'
I didn't used to be so assertive then and I was pushed around more easily, and afraid to say no, but I dug my heels in with this. No WAY was his mother moving in. I would have ended up being her carer. (Not that she needed one as she was only in her early 60s and perfectly healthy! But she would have expected to have been waited on...) Moreover, he has 2 brothers, one was single and lived on his own 5 miles from their mother, and the other one was single too, and divorced several years earlier, and lived 10 miles from her... Both had 2 bedroom properties... Neither one of them was asked to take in the mother. No woman there see. 
@chasegirl YANBU just refuse. Don't be a mug! #BeKind needs to fall off the planet honestly!
oh, p.s. DH's mum carried on living alone for some years and she was absolutely fine on her own. Didn't need to be mollycoddled and waited on hand and foot by anyone. As I said, she wasn't even that old and was in good health!
!