In my view morality is in the act of thinking what is right or wrong. Religion discourages this by proposing rules that should be followed without questioning. So I would expect atheists to be more moral but I haven't looked at any studies that support or contradict this claim.

I tell my Evangelical friends that, "If you have to outsource your morals to a book, you're not read to be talking about morality."

It's because the religious are marinated in the patent nonsense that religion is the inventor and protector of morality. If that were true, then sure, no one without religion (and let's be honest, the specific religion of the person making this ridiculous claim) could possibly be moral. It's typical self-ratifying nonsense from these folks. And because it's not based in reality or empirical evidence, there's no countering it.

What is actually true is that religion simply appropriates morality from its host society and claims to be the inventor and sustainer of something that it didn't lift a little finger to concoct. Morality is a work product of society, and religion has no part in it other than incidentally to the extent it is part of society. For those varieties of religion that fancy themselves set apart from society (in their parlance, sanctified by god), they inherently disavow the heavy lifting done by people outside their own tribe to hammer out the implicit and explicit rules we all agree to live by. It's arrogance and appropriation on a grand scale. But they can't see it.

I don’t think it makes us morally superior it just proves that morality doesn’t need to originate from religion or threats. If anything it’s easier for a realistic person to be/do good without the cognitive dissonance of myths that pit us against each other. I have higher expectations of atheists than theists because we’ve got a major obstacle out of the way already. I’m more impressed by left leaning Christians who despite their ideological deficit still don’t fall for fundamentalist tribalism. That seems like it takes more resolve than being a good atheist does.

Because they base their reasoning on the false premise that without the threat of Hell and the salvation of Christ, you cannot possibly be responsible for your own moral code.
It is of just another veiled threat to back up Religion's unsubstantiated claims of being the guardian of right and wrong.