Most of the Darkfriends are driven by greed and pride (in fact, the element of "pride goeth before destruction, and an haughty spirit cometh before a fall" is prominent in WoT) so they naturally resent anyone better than them at what they do, and, being Darkfriends, naturally see the solution as brutally slaughtering them. Demandred is a special case because, to the extent the BWB is reliable, the only reason he's not regarded like LTT by the ages is LTT, and the differences between their attributes is negligible. He's wise enough it probably wouldn't have bothered him to simply know LTT was the better man, but from the day he was born (which is to say, the day after LTT was) he was seen as "ALMOST the Dragon." How would you feel if you were greater than every man in history but everyone referred to you in terms of someone else because he happened to be just a hair greater? If he's the greatest who ever lived or ever will, and I'm one mote less, well, obviously he needs to go away now.

But if Sammael's hatred of Rand is "a pale shadow" compared to Demandred's, to such an extent even Sammael gives a wry grin at the comparison, how much less is that of renegade Asha'man or even Taim? They think themselves Rand's better as much as Demandred, but unlike him they are SO much less they have no concept of how far wrong they are. You and the ants may be jealous and resentful of your neighbor, but yours is the only resentment that might be justified because you're the only one that might actually BE his better.