It makes no sense to me either. In myth, sirens lure men so it's consistent that this siren would want to use men and keep them tied to her. But why these two men??? That makes no sense, and of course it's just "because it's the storyline and these are our characters" but the show has given us no real reason to believe that and go with it.
She could easily find two other vampires who have less "baggage" to do her work for her. She must adore the drama.
Hot guys + dark subject matter + plenty of violence = watchable television.

Because he is "scorching".
Actually, I think she pretty much said it. Both Enzo and Damon have at various times played her and she sees it as a challenge to obtain complete obedience by any means necessary. It's a pride thing, she is meant to be irresistible.

Never argue with stupid people,they will drag you down to their level then beat you with experience.

Yeah, I don't know why she's working over time to get Damon and Enzo to be so, so loyal to her. Maybe it's a Klaus thing where she wants an army? But she doesn't seem interested in expanding this army
If her endgoal is to just get Cade some bad souls and get food for herself, then what's the deal with going out of her way to hunt down the people Damon and Enzo love? So what if they have significant others. Is she lonely or something?
A rose is just a rose.

Ya plus they seem to only kill those that have done bad things. Out of EVERYONE Damon has done more evil things than anyone..wouldn't he make a better delicious snack than an errand boy? Lol

Yeah it has stopped making sense. I would pick someone a lot smarter. If she wants vampires she could just make them.