1. If God exists, He is a metaphysically necessary being
2. But there are no metaphysically necessary beings that exist
3. Therefore, God doesn’t exist.
So what is the support for premise 2? Well Platonism regarding abstract objects doesn’t seem plausible in some respects. If this is the case, we have good reason to think that at least most necessary entities don’t exist. However, it wouldn’t rule out God because God isn’t an abstract object, He’s a concrete entity by definition.
Someone could argue that it’s likely that no necessary being exists because most things we are acquainted with are contingent. The problem with this is that I could say I mostly experience Apple computers and not Dell computers. Does that mean that it’s unlikely that Dell computers exist?
My concern is that the only reason we have for accepting 2 is to accept that fact that God doesn’t exist, which would mean that the argument is question-begging.