I read a couple of times that Sting and Rouge didn't या couldn't kill their Dragons. I have seen all the ऐनीमे episodes and enough मांगा chapters to know that they are wrong. In the ऐनीमे 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 मांगा that Sting and Rogue only half killed them द्वारा 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 कहा 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 ऐनीमे soon.