Since Planeswalkers were first introduced in Lorwyn, people have been trying to play around them, and to play them to their fullest. A common misconception some players have is attempting to kill an opponent’s planeswalker after it resolves, but before the opponent can utilize it- essentially trying to ‘blank’ their Planeswalker that they just cast! However, unless your opponent makes some subpar plays, that won’t come up much.
The shortest explanation for why that happens is because priority simply won’t let you. The vast majority of the time, your opponent will only be playing a planeswalker during his own Main Phase, while the stack is empty. That means once his planeswalker resolves, he (as active player!) gets priority again. So, they have the ability to immediately activate their Planeswalker, before you get a chance to kill it with a burn spell, or Hero’s Downfall. You can still respond to the activation, but the ability will resolve whether or not the planeswalker is still alive, and the counters have already been added or removed as a cost by then. There is an exception: if your opponent chooses to take some other action first (casting a spell or activating another ability, for example) you WILL be able to kill his Planeswalker before he can use it! But that won’t come up much, sadly.
Today’s Rules Tip written by Trevor Nunez