Can expresses ability or capability.
He can jump over that hedge.
It cannot rain when the temperature is 30 below zero. But it can snow.
might expresses a possibility, something that nothing is preventing from happening or that nothing would have prevented from happening. It isn't or wasn't necessarily a likelihood, but it certainly isn't or wasn't an impossibility.
It might rain today.
He might jump over that hedge. I know he can do it. He seems to be getting ready to do it.
The dog might have eaten your sandwich.
Since dogs can eat sandwiches (probably in just a gulp or two) and the sandwich is gone, it's possible that the dog ate your sandwich. He was nearby when you took it out of your knapsack and laid it there on that log.
The dog might have phoned your sister to say you were running late. How else would she have found out?
-- The dog can't have phoned my sister. He does not know her number and it is unlisted.