And remember, I don't have to prove anything because you can't prove a negative. You can't prove unicorns don't exist, you can only indicate that you've never seen one. That doesn't mean you must accept their existence until someone proves conclusively that they cannot possibly exist.
That's a red herring, a straw man argument, A_perfect_lady. Whether or not unicorns exist is entirely beside the question. It hardly seems to be an urgent question from my point of view.
But if you want me to hazard an answer, I'd say that unicorns both (certainly) do and (possibly) do not exist. Certainly they exist in the human imagination; i.e., in the arts, in literature, etc. the unicorn historically/culturally is a symbol of purity. What you are really asking is whether they are physically tangible. And I don't know the answer to that. All I can truthfully say is: I have never seen one.
I don't "group" atheists. If there is a "group" for atheists, it is something atheists self-select into. I don't force them into it.