Requiring someone to provide evidence to back up a claim is not the same as taking a position that the claim isn't true. This is the root component of the burden of proof and the stance many people have towards a god claim: they aren't convinced the god exists due to a lack of evidence provided by the person claiming the god does exist. Until there's actual evidence it's rational and reasonable to withhold judgement.

The unicorn (or other mythological beings) are used as a similar case to illustrate to a theist that they have the same kind of attitude towards the idea of a unicorn existing as an atheist does to any gods. They're both neat concepts, but without evidence showing they actually exist, they're nothing more than an idea for stories and art.