Or they were taught before the time skip. They might have been around the time Wendy was taught as well. As it seems dragons didn't teach humans synchronically. They disappeared at the same time though. Those kids might really think they killed their dragons, but we can't know that.
Another theory is that the dragons for some unknown reason told them/allowed them to kill them.
I do think its more likely that they disappeared and Sting and Rogue just assumed they killed them somehow. Most likely they are the same age as Wendy when they started training with their dragons and were too young to fully understand what really happened
Either they were deceived by their dragons so that they could join Sabertooth for a home.
Or they were able to defeat their dragons with the power of their dragon force because they can go into dragon force by themselves. They would not be affected by the dragon's element either because they would be able to eat it.
And they would stand no chance against Acnologia. That thing is not a normal dragon. It is the apocalypse (just as it is called).
I'm pretty sure the only reason they can enter Dragon Force on their own is because of the lacrima that is implanted into their bodies. Its been shown that you can only enter Dragon Force by absorbing another source of magic power, like when Natsu ate the Fire of Rebuke or ate Laxus's lightning while fighting Hades.
I also believe that you will either see some sort of team up between the Dragons and Dragon Slayers against Zeref and Acnologia since those two seem like the major villians in the series. Something along the lines of Natsu eating magic from all the Dragon Slayers and maybe even from the Dragons themselves to do it or the Dragons will team up to take out Acnologia.