Why, when people are angry, do they say "I was all but angry" as opposed to "I was angry"? What's the difference between the two and why are they used interchangeably?
"All but" is (rather old-fashioned, in my view) idiom, meaning "nearly".
I don't recall having heard "I was all but angry", but to me it means "I was almost, but not quite, angry".
Actually, "all but" literally means "everything except". When you say "I was all but angry" what you are really saying is that you are everything except angry, or that you are not angry. It is usually used in the exact opposite sense, though.
According to the grammarist website:
All but is a compound adverb that means almost or very nearly. Be aware that it is also used without being a compound adverb to meaning everything except.
As an example, consider that I paid a $1000 damage deposit when I began renting, then I recently moved out and made the following statement:
My landlord returned all but $100.
He actually returned $900.
My main point is that I would never be too sure what someone means when they say "all but" unless I consider the context.