disarm only

It was said in the last film that the reason Harry was the owner of the Elder wand was because he disarmed Malfoy in the first part of the finale. And the reason Malfoy is the owner despite Snape being the one to kill Dumbledore, is that Malfoy disarmed Dumbledore first. So, what I got from this was that disarming practically meant that you either own a new wand or lose your own.

My question is, why wasn't this a much bigger thing in the earlier installments? I don't really remember somewhere where they mentioned that disarming somebody could mean gaining ownership over the wand you disarmed or ultimately losing yours. I do remember the lesson of disarming in the second movie where Malfoy and Harry were pit against each other. Though their wands never really got flicked out of their hands and rather they just got flung around by the spells, so maybe that doesn't count.

It's just strange that some of the strongest wizards in the wizarding world got duped because Malfoy failed to mention that he disarmed Dumbledore and then got disarmed by Harry in the second to the last film.

.....maybe I should read the books because I have a feeling this is going to bug me for a long time.