I read a couple of times that Sting and Rouge didn't または couldn't kill their Dragons. I have seen all the アニメ episodes and enough マンガ chapters to know that they are wrong. In the アニメ 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 マンガ that Sting and Rogue only half killed them によって 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 発言しました 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 アニメ soon.