Is it possible that some people can lavish kindness and compassion on others, but they are unable to do the same for themselves?
A step further in this reasoning might be that some people show compassion for others because they are not unable to do it for themselves.
Compassion is not pity, nor self-interest. Compassion is the desire to bring help or relief when we are confronted by suffering or pain. While such benevolence is acceptable when directed at others, some people might think that doing it for oneself is not acceptable.
We benefit in all sorts of ways when we are compassionate. Genuine caring and doing things for others produces hormones associated with pleasure and bonding. It can make us more resilient to stress, more caring and, in short, better people.
But if all our efforts are directed outwards, while it might earn approval and even get us a gold star or two for being nice, to become a better person you also have to care for yourself. Consider self-compassion as a contributor to your own wellbeing.
Article and video What is Compassion.