Note that you did not provide a logical explanation for the claim "God doesn't exist", this is very important to remember.
I'm motivated by my trust that there is truth that can clear up my understanding of the world around me, including my understanding of myself as an existing being. This is not how skeptics approach the world. They approach the world with the belief that every truth claim should be doubted, except for the claim that they themselves should always be skeptical, that should never be doubted.
However, the truth is that they should doubt whether or not being skeptical all the time is actually a rational way to figure out the truth. Logically, if I'm always doubting truth claims then I'll never accept the claims that are actually true.
We should be able to trust that logical explanations can and do point to the truth. If we can't trust that basic understanding then we might as well stop thinking because figuring out the truth is hopeless. UNLESS your goal is not to reach an understanding of the truth, but rather be skeptical of all truth claims, then maybe you are hopeless.