It's not a non-sequitur. The usual reason people believe in a god is because some religious group says that the god exists. Those religious groups usually also claim that their god is good. If they're wrong about the goodness, why shouldn't they be wrong about the existence too?
"God exists and he is good" is mentioned as fact. The evidence of the existence of God would be his goodness - call it miracles if you will.
In a world where you perceive the absence of this goodness removes the only evidence provided. The logical consequence is not that god exists and is malevolent, the logical consequence is that the goodness is not there because God does not exist.
The 'miracles' can easily exist alongside his badness. I'm not sure why everyone makes it out to be either/or. There is no universal law that says being both can't logically be true. I mean, there's an easy way to prove this. If I said humans exist and humans are good, you could point out Hitler, and all it does is prove humans are good and bad, and doesn't test whether they exist. And in fact it doesn't even prove that they aren't good, just that they are also bad.
So if someone says "god exists and he is good" and all you end up doing is disputing the second statement... you didn't even touch the first.
When people say that "god isn't good, therefore he doesn't exist," they are very likely referring specifically to the Abrahamic God, and this is likely the only God they can conceive of as possibly existing.
Of course you're correct that, in the abstract, the set of potential divine deities is infinite. But most people in the Western world turning away from religion are turning away from some flavor of the Abrahamic religious complex.
It's interesting you bring up the Abrahamic God, because the old testament specifically describes Him as, among other things,
- Jealous
- "Full of wrath"
- Vengeful
- Willing to harden hearts (make people resistant to obedience)
- demanding and severe
- prone to tempting or testing people
These are not my pejorative statements, but the literal language used, at least in the English translations. It seems the idea that the Abrahamic God is just trying to make everyone's life better all the time is a more modern western invention. I don't think it was common even 150 years ago.
There are a lot of problems with trying to tease a coherent overarching narrative, much less a coherent morality, out of a canon that has nothing of the sort. There are part of the Old Testament that were likely written before the Israelites were even monotheist. The Gnostics found the contradiction so irreconcilable they decided the God of the Old Testament was really an evil god who created our fundamentally flawed material universe as a prison.
There is no "God" of the Bible per se because the "Bible" itself is a, dare I say it, social construct and "God" is a mirror that people hold up to reflect their understanding of nature and morality, and that that context is always subjective and transitory. To me that conversation that humanity has with itself over time as it tries to reconcile a chaotic and arbitrary universe is far more interesting than anything one learns in Sunday School.
That depends on how once conceives god. For instance, Anselm defined god as a being than which no greater can be conceived. If one accepts that definition, it is in fact a sequitur.