Why do abusive parents think you are obligated to care for them?

Stick to your guns.

Basically, abusive people in general think the world owes THEM a living. They have little to no empathy or the ability to put the shoe on the other foot and consider how THEIR behavior affects, or has affected, OTHERS. So she may feel like you owe her, which doesn't make it a fact, just an abusive person's way of looking at things. Your 'auntie' probably wants nothing to do with your mother so she calls you 'heartless' and such so you'll be guilted into caring for a mother who you want nothing to do with.

If you've cut your mother out of your life & want her to stay out of your life, leave things right where they're at. Let your auntie know your decision and move on with your life now. Nobody can judge YOU until and unless they've worn YOUR shoes.

Good luck!

You’re definitely not obligated and I hope you won’t discuss the subject any longer with your aunt. You’ve said no, that’s a complete answer and you don’t need to explain or justify your decision.

As it is said a lot on this site "NO" is one sentence. No need to explain. Also "guilt" is self imposed.

You are in no obligation to care for Mom. If she needs LTC, your Aunt can turn Moms care over to the State. Things will get done quicker that way.

They feel entitled, like everyone owes them.
It's similar to how some people want everything for free.
Plus, they feel, they did it for you, now you help back. They don't understand it's different. It's hard to care for an elder, while caring for your own family. And it gets harder own time.

Because they are narcissists and they are used to the entire world doing their bidding or ELSE. Because they are the Abusers and the rest of the world is the Abusee.
Tell "Auntie" she is more than welcome to take her sister in, and care for her.
So, you are one of the SMART ones who walked away. GOOD FOR YOU. I hope you have made yourself a quality life. There is no way on earth to make up for what you have missed in a parent, but there is a good way to make FAMILY out of quality people who exist in our world. I am so proud of you. It is no easy task to move out of the target area of these people. It is a habit to believe you are worth nothing but the abuse they level.
If you are of a mind you are free to tell your Mom that you hear she isn't feeling well and you wish her the best. For myself I might choose to stay well out of her aim.
My very best to you. I hope you will stick around on Forum for DAILY we see pleas from caretakers who were abused all their lives and now feel obligated to take care of their abuser. You have broken free. You know how very hard it is and how much hurts still and how easily wounds are reopened.
Again, you should be so proud of yourself. Tell Auntie to go fish.

Abusive parents almost never realize they were abusive. And if you do bring it up to them, three things can happen:

1. They deny all of it.
2. They shrug and say "well, we did the best we could!".
3. They'll gaslight. "Well if you'd been a better son/daughter, we wouldn't have to have been so hard on you!".

In short, you can't win.

Often abusive people are egotists and the classic egotist is always right, good, deserving, etc.

If your aunt is concerned about her sister, then she should get busy and work on placement, etc. You are actually doing them a favor by saying a firm "NO" - that way the situation is clear and they can proceed to find other options.

They like having you around so they can keep abusing you.