Can someone please explain why I find this line so funny?

Probably because of how absurd it sounds from our current timeline where brain shelters don't exist yet.

Or maybe it's reminding you of Richard Nixon from Futurama lol.

Because "brain is being housed in the brain shelter" could be misinterpreted as "brain in skull."

Like saying "bread tastes better than key" or "because the coal was thirsty."