Never ASSUME because when you ASSUME, you make an ASS out of U and ME.
Today's quote is an often repeated one. I actually didn't know this quote was attributed to anyone. I thought it was just a saying. However, it seems Jerry Belson has been credited with it, though he said he heard it years before from a teacher in a typewriter repair class.
The quote is often used to criticize someone for making an assumption. If someone assumes they know what is going to happen, you can say, "You know what they say: Never assume because when you assume, you make an ass out of you and me."
The quote just takes the word ASSUME and breaks it into three parts (ASS, U, ME). Then it takes those parts and constructs a sentence. The great thing about this quote is that it is accurate. If you assume something, it might not come true. This might make you look like an ass (idiot).
I believe the word ASS in this quote is meant to refer to a donkey. Since it is also a bad word, it is often used as an insult. Donkeys are assumed to be stupid, lazy, and stubborn. So, if you call someone an ASS, you are saying that they are stupid or a jerk. If you say, "you are making an ass of yourself," you are telling them that their behavior is making them look stupid or like a jerk.