why do my chrysanthemum buds die before opening?

welcome to GOY.
is this a houseplant? if yes its because it is getting too dry. I find they need to be cool and moist . try misting the plant or stand the pot in a gravel tray that you water.
if it is an out door/garden plant then i dont really know. though it could be lack of rain.

If it's an indoor one, it won't like central heating, so keep it in a light, cool room away from radiators, etc.

I grow lots of mums, both outside and in the greenhouse. You have bud rot. Throw away the infected plants because you don't want this to spread.