How many times have you been asked by a religious believer about your argument against the existence some sort of god? Yeah, me too. What many religious believers seem unable to grasp is that no arguments are necessary on the part of the atheist. The atheist position is simply that those who believe in gods have not provided sufficient evidence to support the belief claim they are making (i.e., some sort of god or gods exist). For most of us, atheism is the rational consequence of the theist not meeting his or her burden of proof. It really isn't any more complicated than that.
When someone tells you about something that sounds so implausible that it is unlikely to be true, you ask for evidence. If the person provides you with sufficient evidence, you may begin to suspect that their claim is valid. You may begin to believe what they believe on the basis of this evidence. In essence, you scale your belief in a manner proportional to the evidence provided. On the other hand, if they do not provide sufficient evidence, you remain skeptical of the claim(s).
Since this does not seem to click for many believers, I often find myself saying something like this:
I do not believe in gods for the same reason you do not believe in unicorns. You do not have an argument against the existence of unicorns; you need no such argument. You simply realize that there is insufficient evidence to support their existence and so you do not believe in them. And you are absolutely right to do so.Atheism does not need to be any more complicated than this.