Mysteries and Investigation: A dm can be perceived as adversarial when the things the players try are shut down. It's complicated, because the dm might just be trying to play the world in an accurate way, but the result is that the players find that they can't do anything. Or the players come up with a plan, and to the dm it is not a great plan, and doesn't take into account a lot of information, but the players don't realize that. Mystery/investigative scenarios falter for this reason: the dm thinks they they are giving plenty of clues, and the clues are obvious, while the players are totally stumped because they actually have very limited information. I think the way to address this is 1) be a fan of the PCs and 2) be very generous with information.
Traps: Gygaxian traps are notorious for being gotchas, where there is no or very limited ability to notice the danger you are walking in to. He exacerbated the problem by getting annoyed at players for being overly cautious. 5e traps are more like a perfunctory skill check combined with a slight annoying hp/resource tax. I'm not even sure the osr has solved this problem, for all the talk of "player skill." Either the traps are deadly enough to really put the "crawl" in dungeon crawl, or they are a resource tax (though, that's maybe more significant when resources (e.g. HP) are more scarce). Chris McDowall has some
good thoughts on this.
Combat: Is combat-as-war, with unbalanced encounters, unfair? There are some that might say that even combat-as-sport, where the dm plays the adversaries in a tactical mini-game, is overly adversarial, and that a dm must balance their encounters and adjust on the fly to make sure the PCs don't die. Then we get into what someone on another thread called combat-as-performance: the dm plays out the encounter for maximum drama and so that the players feel like heroes, but in reality there was no danger to their characters. I've presented players with balanced encounters that they defeated, but to them it felt adversarial because it wasn't easy, and because I was rolling in the open and playing tactically rather than merely narrating their successes. I'll be honest I have no idea what to do when players want combat-as-performance, often because admitting that that is the desired playstyle breaks the
illusion of combat being any sort of game challenge (whether as sport or as war).