I always thought it boiled down to two things:
-Mass Effect 3, as a whole, is kind of a mediocre game. It wasn't a fantastic game marred by the last 10 minutes, it was a game with a bad start, a middling-to-good middle, and a bad third act (which I'd classify as starting with Priority: Thessia). It's a game where the mission and story structure feels very rote and "just-so," in an attempt to neatly tie up every plot thread. Sometimes this works out mostly well (Tuchanka and Rannoch, which are the high points of the game by far); a lot of times it doesn't (running around the Citadel listening to people wish they had artifacts you'd go play Space Pac-Man or run through a multiplayer map to find; random sidequests for ME2 squadmates or old NPCs that mainly served as "remember me?" moments).
-The ending itself was super contrived. The means are contrived (humans find the plans for a Reaper Off Switch on Mars and start building it without knowing what it does or how it works, it operates via space magic, it does three highly specific borderline magical things with convenient nodes at the end of each walkway but they 'unlock'' via a readiness system that doesn't really seem to line up with how it works), the way it's conveyed is contrived (a hologram representing a ham-fisted symbol for "you can't save everyone" robotically explains what the point of everything is and your choices, while Shepard stands with a dazed expression, unquestioning the entire time), the conflict is contrived (organics vs synthetics is merely one conflict among many in the galaxy, and one you could have made significant inroads on; if the underlying theme is "created vs creator," then where do the rachni stand? The krogan were uplifted, do they count as "creations" who need to be purged? What about genetically enhanced people like Miranda, or intentionally created biotics? No, it's all specifically about robots with computer chips for brains; never mind that none of the three options actually solve this supposed problem at all). Then a magic explosion happens and you're supposed to just go, "oh okay, something bright and shiny happened, so the story is over and the problem is solved. My crew is on a space jungle now, I guess that represents the Garden of Eden or something to symbolize a new world starting, but I shouldn't think about this at all."
Oh and the final image of the original ending was a text box pop-up telling you to buy DLC.
edit: I suppose if I had to list a third thing, it'd be what others have brought up: the ending, both through intention and accident, seemed to completely "end" the universe that the player had gotten invested in. The intent was that it ended by an act of rebirth, being replaced by a brave new world following the choice you made; the accident was people pointing out that what was literally portrayed on screen would logically result in a massive amount of death and suffering, if not the wholesale destruction of the galactic civilization you were trying to save.
These two posts sum it up well.I mean, the entire mechanism at the center of how the game ends, the Crucible, is a complete nonsense device. How does it work? Why does interacting with it in three completely absurd ways (blow up a component with a pistol, grab a conduit and disintegrate yourself, swan dive into a beam of light) result in any of the endings you get? Why is the Crucible even built in a way that would allow more than one option in the first place, regardless of how insane any of the triggers are? Why didn't the console you first try not work, only for there to be a conveniently placed elevator that took you up to a platform where all of this ending nonsense plays out?
Never mind Star Child being there to condescendingly tell you to use the damn thing you were already there to activate in the first place. Seriously, just forget the color of explosion for a moment. The entire concept of the Crucible falls completely apart if you think about it for even a few seconds.
I'll add to them that the final turret sequence, in the middle of talking to your squadmates before the final showdown, is emblematic of ME3's design issues.