I read a couple of times that Sting and Rouge didn't или couldn't kill their Dragons. I have seen all the Аниме episodes and enough Манга chapters to know that they are wrong. In the Аниме it is not yet proven that Sting and Rouge really killed they're Dragons: Skiadrum and Weisslogia.
The truth is that Sting and Rogue really killed Skiadrum and Weisslogia, but half killed them. It is mentioned in the Манга that Sting and Rogue only half killed them by that I mean, they didn't really kill them.
In Sting's case, Weisslogia told Sting to kill him, so Sting can prove that he is a true Dragon Slayer and also сказал(-а) that a Dragon Slayers power increases when it touches Dragon blood.
And in Rogue's case, Skiadrum was sick and was going to die anyway.
Sting and Rogue are half true Dragon Slayers and it will come in the Аниме soon.