Zolo wrote:*** WARNING: SPOILER SPECULATION HERE ***
I suspect he hatched a plan to sacrifice himself to allow Snape to gain Voldemort's full trust. When he confided his plan with Snape, that's when they got into their huge argument. And since Snape knew he'd be a marked man as soon as he killed Dumbledore, I think that's why he got REALLY pissed off when Harry called him a coward.
Yep, that's exactly what I thought as well. And Dumbledore was begging Snape to kill him, not to not kill him.