Slyrak slyly sliced Davion

It was so he could inhabit Davion's body. He was dying, so rather than die, he basically put his essence inside of Davion to live within him. Here: https://dota2.fandom.com/wiki/Dragon_Knight/Lore

That would be like a human asking an ant nicely to please get out of the house instead of smashing it.

Dragons see humans the way humans see ants. Tiny and insignificant.

Could have been he didn't have time to discuss/negotiate it, or deal worth the possibility that DK would have said no. Slyrak was dying and only had seconds to react.