I'm playing on a realm with some friends, although I think the problem might be present in bedrock and not only on realms.

It happens that I am breeding horses to get a perfect specimen, and I found that a horse had grown up. I started taming it, and it looked very promising.

It had 13 heart points, but when it threw me off, I accidentally hit it with my pickaxe (dealing 10 damage points). When I got on it, to continue taming it, I saw that the max health had gone down to 8 hearts and it stayed that way after being tamed.