If you have a "fuck to give", it means you actually care about the situation or problem, which is generally rare. A "fuck to give", can also quickly disappear.
When you don't have a "fuck to give", you have no intention of caring about anything that relates to the problem/situation/statement.
When you are all out of fucks to give about anything at all. Or when someone states the obvious right in your face so hard that a fuck would be wasted on them.
"Easter was last week..."
"I haven't a fuck to give."