Considering that means "it does not follow", I don't think you understand how to use it. He claimed morality has an ultimate source. I pointed out that if morality had an ultimate source then globally morality would be uniform. Since it is not uniform, it would follow that there is no ultimate source for morality. In other words, the EXACT opposite of a non sequitur.
Again, by appealing to empathy, you are giving up on logic and reason in favor of some arbitrary belief.
Society thought slavery was fine 150 years ago. If it were to do so again, atheists would be entirely unable to defend their position without the dogmatic claim that "slavery is wrong."
Yes, atheists, while inherently trying to use logic in reason, are still human, and are still capable of and at least partially driven by empathy. Most people who aren't narrow in their view can see how logic and empathy can work together.
You made the comment earlier about the "dogmatic claim that all men are created equal". Yet the Bible itself disagrees with that. Many in the Bible are created lesser. Think the Curse of Ham, or this gem
"All the people who were left of the Amorites, the Hittites, the Perizzites, the Hivites, and the Jebusites, who were not of the people of Israel their descendants who were left after them in the land, whom the people of Israel were unable to devote to destructionthese Solomon drafted to be slaves, and so they are to this day." 1 Kings 9:20-21
The entire concept of people ACTUALLY being treated as equal arose as people stopped taking the Bible literally and began considering empathy OVER scripture. Hell, the concept of using empathy in place of scripture based morality is the core of what being an atheist is. To claim that slavery is wrong is a dogmatic claim is bullshit. Slavery is all throughout the Bible and is justified within it constantly. True equality amongst humanity comes not from following God but from rejecting him. And your "what if" scenario of if society moved to being ok with slavery again simply won't happen, because as a society we're moving away from religion and therefore we won't have a dogmatic claim as to justify slavery.