So far it seems that the Six fingers are working for Baal, who is leading some sort of revolution to force demons back to an age of war and chaos. Back to their origins
Shiida seems to care for Iruma, but Baal (and therefore the Six fingers) need Iruma to stay alive for some messed up project involving "bringing back the King Delkira" and using the King's power for their own plans.
Six fingers don't dislike humans, they consider them fancy food and probably know the power boost feeding from a human can be. Humans are cattle to them and therefore useful to have. I think.

Wait what’s the six fingers motive? I think I missed it or they didn’t mention it. Why did she want to protect Iruma that is a human didn’t they dislike humans ?