Cup Of Liquid
Counter For Cups
A tree is not a cup of liquid or a counter for cups. Don’t get them mixed up. The last time you tried making a cup out of a tree to count your throat got filled with splinters when you used it. There wasn't even any liquid in it.
Another way to remember the counter for cups using a cup of liquid would be by creating and memorizing a haiku (はい) about them. Aren’t haikus useful?