Some cats like it and some only allow it, but it's very common that they prefer not to have our faces in their faces like that.

The cat headbutting you on the chin or nose or whatever is fine, but returning the favour (with or without kisses) is a different thing entirely. It has to be their choice to get in our face, not the other way around.

My guess is that we have such large faces with such large eyes and mouths that it triggers some built in discomfort when they're not prepared for it to come up so close from above, like some large flying predator... or maybe it's the smell of human mouths that becomes overwhelming.

Or maybe they consider themselves the adult in the house and will not be groomed by us slobbering babies.

Or maybe they're just divas who need everything on their terms at all times.

Either way, I will still kiss them on the head... but I'll hold off until I've gotten enough cuddles to last me a while, knowing they might flee.

Perhaps kissing their cheek or chin is more acceptable?