Falling out is defined as a disagreement or something that causes two people to no longer be friendly with one another.
(noun)An example of a falling out is when two sisters fight over their inheritance and stop speaking to each other.
See falling-out in Webster's New World College Dictionary
noun pl. falling-outs or fallings-out
See falling-out in American Heritage Dictionary 4
noun pl. fall·ings-out or fall·ing-outs