Expressions that "don't make sense" are often the product of misunderstanding or defective cultural transmission.
He wants his cake and eat it too.
Of course he'd want to eat it! What else is he going to do with it, wipe his ass?
The expression is, or at least was: "He wants to
eat his cake and
have it too" -- i.e., to eat it and still have cake to eat. The meaning is clear and coherent: to want both of two incompatible things. But the expression has become commonly garbled to "He wants to
have his cake and
eat it too" (not to "He wants his cake and eat it too," which is not even grammatical), which is senseless, since of course you have to have your cake before you can eat it.
"I could care less." (not really probative of anything)
Indeed, people say that, but I have always assumed that it was just a garbled version of "I couldn't care less," which makes perfect sense.
Another expression that has suffered from garbling is
"The proof of the pudding is in the eating." The expression is pithy and has a clear meaning, especially if you understand that the word "proof" here means "test." The point of the expression is that the way to find out if some product is any good is to do with it what it is made for. But the expression has become widely garbled as
"The proof is in the pudding," which is as senseless as it is witless.