On premise 3, "If the brain is the source of morality and goodness,"-- I don't think anyone claims that the brain is the source of morality and goodness. This statement is vague. One may use a calculator to figure out how much money one has, but (unless one is an accountant by profession) a calculator is not the source of all one's money.
I think you are pointing out that we use reason to figure out right from wrong. I agree with you here, and I see where you're coming from. Reasoning is, indeed, made possible because we have brains. But this doesn't mean that everything based on reason thereby has the "brain as its source". Pythagoras --and/or his follower(s)-- discovered the Pythagorean theorem. Now, he/they obviously needed their brains to discover the theorem. But the theorem is not made less valid because we don't completely understand neurobiology. You can do one of those proof thingies and figure out that it works.
I think you are pointing out that we use reason to figure out right from wrong. I agree with you here, and I see where you're coming from. Reasoning is, indeed, made possible because we have brains. But this doesn't mean that everything based on reason thereby has the "brain as its source". Pythagoras --and/or his follower(s)-- discovered the Pythagorean theorem. Now, he/they obviously needed their brains to discover the theorem. But the theorem is not made less valid because we don't completely understand neurobiology. You can do one of those proof thingies and figure out that it works.