People in houses now who bought years ago, particularly in the SE, have made an absolute fortune on their home. They might have 'worked hard all their lives' but in my parents' road there are elderly Police officers, teachers, people who worked in banks, most of whom had SAHM/one income. To buy one of those houses now, you would have to be a millionaire or two very well paid workers. They didn't 'earn' that money, it was a fluke of the market. They certainly wouldn't be able to have the same house now.
The money for their care has to come from somewhere. Why should I get 100Ks instead of that money going to fund their expensive care if they need it? Just because my parents lucked out on their house? It's like musical chairs but with people's futures.
You can't argue you want equality in provision of free care but not equality with intergenerational mobility.