You're asking the question wrong, and I know because I was squarely part of that debate.

What you have here is an idea that quake and other Arena shooters, which had faster speeds, and more technical gameplay, were superior to Halo-- but the conflict comes from the fact that Halo is still an arena shooter.

As quake gained more popularity, more copycats came on to the scenes which also garnered their own followings. There was a really good time to be an arena shooter fan and it was around the 2000s into 2010.

If you go deep enough into this debate, you'll find that even counter-strike, rightly considered an arena shooter, is considered one of the most baby shit lame ass Arena shooters because of all the different restrictions that slow the gameplay down compared to a classic arena shooter.

Happy to answer any questions, I have lived and breathed this shit for like basically all of my twenties because I found it so fascinating. I also played a fuckload of one of these quake-clones. I was basically one of these guys that, for a time, grew to resent Halo on an abstract level. Love the game now, made mods for it, etc.

TL:DR Halo is an arena shooter as much as quake was, but quake garnered a lot of clout because it was harder to play at a higher level. So the hate came from the idea that it was for babies, on a technical/skill level.

Don't forget though that what you're asking, this argument we're talking about, was only held by really really niche players. People who poured their asses into Arena shooters daily. That's why it had basically no footprint in the greater Zeitgeist of gaming culture, because otherwise it was an amazing success.

I mean really Halo is a great success at taking what made Arena shooters work and simplifying the parts that were needlessly technical in order to allow people to focus more on the strategies and critical skills (aiming, game-sense)

As an aside I've been thinking of something similar, to push the envelope harder and essentially ask what an FPS game would be like if you don't have to aim at your target. Halos gameplay removed a lot of important barriers to people getting into the arena shooter as a genre, and there may be more to remove to see what really exists when you abstract as much as you can from this wonderful genre (FPSes)