First off, if there is an atheist argument from non belief why not a theist argument from belief?
That people believe doesn't equate, with the depiction of god, to any sort of reliable conclusion that therefore a god is real.
Any way this seems to say If God we’re all loving he would want everybody to become a believer.
That's a part of it, yes. The presumption is (and, indeed, the explicit message from many religious believers is) that believing in a god, accepting the premises of the religion makes you a better person. Some version of an eternal reward is normally involved, which is depicted as to the benefit of the believer, which an all-loving god would be presumed to want on the believers behalf. Therefore, if an all-loving god is creating reality, why is it creating a reality in which people might not believe and might be denied this; it's a variant of the problem of evil idea, I guess, and is probably best countered by the idea of free will and that the reward is only worthwhile if it's somehow 'earned' or 'deserved'.
Is that an atheist argument?
I don't think it stands up well on its own, I've seen it used as a counterpoint to the idea of free will - the idea that god had already, in giving us free will, decided that some would be lost which doesn't jibe with the idea of omnibenevolence.
I’m not sure. It seem’s to revolve around what God considers belief
It hinges (as do so many things) in Christianity at least on what's required to achieve 'heaven' - if it's at God's whim then how we live is irrelevant, if it's 'earned' then why are the instructions so vague, contradictory and in places immoral (or, silent on immorality)... there are probably other mechanisms posited.
Another strand is that God should be reachable by pure reason.
That, I suspect, is a result of people who in theocratic times were forced to justify their non-belief coming up with arguments that then needed to be countered. In the overwhelming majority of cases it seems that believers do not come to their belief by reason; for those who come through childhood without being indoctrinated/inculcated into a religious tradition, the methodology needs to change for religions to claw those few errant souls back, which is where attempts at reasoned arguments come in.
Again, who is perfectly reasonable?
Should we then abandon the arguments from morality because who is perfectly moral? Should we abandon the arguments from contingency because free will means that none of us are perfectly contingent?
O.