whilst others who didn't buy their own homes get their care paid for by others
You could use the same argument about home-ownership in the first place. Why should anyone buy their own home, or get a job even, when others "get theirs paid for" in benefits. People want to own their own, for security, and autonomy and choice as to how to make it comfortable.
People are already desperately trying to find ways to transfer their properties to their children to avoid this. Yes, and it's called 'deprivation of assets,' and the authorities are clamping down hard on it.
No matter your opinion many people will continue to feel this way
Am I not allowed to express my opinion, then? It's called debate.
And in the interests of transparency, we have just sold my dad's house, now he is in a care home. He was fully in favour of it, and with our support, was able to choose a fantastic place (but we would dream of "only" paying £1000 per week!! Get real, people!)