You didn't play the old system nor were you good in the old system though, so you can't exactly understand his PoV, and the truth is - the old system WAS more fun.
It actually kept some order in the game and dictated what healers can play what comps. Right now, if you have a combination of melee that's op ( let's say that DK Rogue becomes stupid OP in next 2 months ), you just pick the best healer, and everyone who can multiclass just swaps over to that healer, not unlike people in League of Legends swapping from Akali to Diana because one is simply a better version of the other.
In the old system, double melee for example COULD NOT play with a Resto Druid, no matter how OP Resto Druids were, simply because they would sit in novas, roots, slows, and get nothing done. So double melee was forced to run with a different healer that allowed them to stick to targets but didn't have the output of a Druid that would allow them to be immortal thanks to their healing mechanics and other stuff.
In the old system, you had like 5 things you needed to counter, and most of the popular comps in meta only had the tools to counter 3 of them, maybe 4. In the new system, everyone has the tools to counter everything, partly because healers are made that way, partly because DPS classes got homogenized, resulting in a considerably less fun game.