Ok but what if morality is subjective..? My morals say that killing puppies is bad, and people who do it are bad.

But with universalism, killing a Nazi is bad. Because it's killing. With universalism, humanity is attempting to assign intent to the universe and say that the natural state of being for morality is that killing is bad. It's simply not true. Perhaps in most cases, but not all. That's not universalism, by definition.

Am I woefully misunderstanding something here ..?