Telling someone I am an anarchist provides a shorthand for letting them know that I am opposed to the infrastructure that supports our society like capitalism, the state, patriarchy, etc. I find it is easier to do that than to say "I am opposed to the infrastructure that supports our society, such as capitalism, the state, patriarchy..."
In addition to efficiency (and it isn't always that efficient in the long run), saying explicitly that I am an anarchist separates me from the progressive/lefty crowd who are opposed to capitalism, the state, patriarchy, etc. but who would prefer to legislate, peacefully protest, have discussion groups, make consciousness-raising art and vote away the Very Bad Things, as opposed to attacking them directly.
What makes this not always efficient is that sometimes the progressive/lefties call themselves anarchists too and think that I want to legislate, peacefully protest, have discussion groups, make consciousness-raising art and vote away the Very Bad Things. Sometimes those who would not call themselves anarchists at all think that saying that means "I listen to punk rock and don't like washing dishes" (in my case only the first half of that is true). In these cases more conversation is required.
As far as the limitations beyond all that, I definitely meet folks who think we are on the same page because we use the word anarchist, when in fact we are not (anarcho-syndicalists, an-caps, many more dogmatic a-p's), but that doesn't actually worry me. Words (and language) are going to be limiting. There can't possibly be a word that encompasses the entirety of what an individual is, but anarchist is a pretty good word for describing what a person is against.