Walking Dead: Why Carol killed Karen and David....

So after this last episode I think I finally understand Carol's flawed thinking on why she killed Karen and David after they contracted the flu.  It never made sense to me before how she could justify it and not understand that what she did was not only premature, it wasn't her decision to make. She said to Daryl in the last episode on Sunday (Consumed) that you don't get to save anyone anymore. I think she felt that after they contracted this flu that they were already dead.  And she killed them because it's like after you get bit by a walker, you kill to stop them from turning into walkers.  She saw Karen and David as dead, because you can't save anyone anymore.  And since they were dead already it only made sense in her mind to put a dagger through their brain so they don't turn. And in this last episode it seems like she was realizing that it's not so black and white.  You can save people, and at the very least you should try.