It's primarily just a staple/pillar of WOW since it was introduced; kill boss, stuff drops. For those of us who have been playing a looong time, it feels a bit unnatural and/or disconnected with the LFR changes to personal loot. Did anyone get anything cool? Did anyone get anything at all? We don't know. It's not a matter of being selfish or greedy and then being pissed about "OMG MY ITEM! HE TOOK IT!". It's just about being curious to see what dropped, and who won.
It sounds like you're a bit upset about losing "your" item(s) to someone, as if they were ever yours to begin with. For all you know, they could have been after them for as long or longer than you. If a rogue took your tanking trinket or something, then that point doesn't hold any weight, but just because you want something doesn't mean you deserve it more than someone else. RNG has always been a part of WOW, especially in loot.
Personal loot allows for a wider array of options in gameplay (such as flex-raid, since scaling "normal" loot drops in that raid-type would be incredibly difficult), and certainly weeds out the potential for ninjas or greifing. But the downside that he is referring to (IMO, anyway) is the departure from "tradition" in the name of pandering to the newer generation of WOW players/gamers who just want everything now.
But I'm probably just jaded, from playing since the dark ages