I was one of the rare folk who loved it from the beginning, and have the posts here on the BSN to prove it 
(Getting to this thread late - after 5 playthroughs and a platinum trophy I've seen this game in and out, and I'm largely out of the fandom until I hear DA5 announced.)
Others have dissected the fan reactions here. I do have to note that about a month before DAI came out, fan judgments out of the gate on DA2 suddenly became a lot more friendly. See up until the release of DAI, DA2 was the evil game, the proof that BioWare had jumped the shark. I had liked that game too, and was defending it. Then just before DAI came out, there was an explosion of threads on the BSN about how DA2 was a good game and unfairly maligned. It was like folk were saving up their bile and rage for the next entry in the series.
I've seen this dynamic before in the Final Fantasy fandom. I'm old enough to remember that Final Fantasy 7 was widely considered by fans to be jumping the shark because of the extreme genre shift. It's now considered one of the greatest video games ever made, but every sequel has been terrible and a disaster...until its sequel comes out and rehabilitates it.
I think it's something about internet culture. People seem almost afraid to admit they like something. Is it a fear of hoping something will be good, and being disappointed? Is it because bad reviews are more entertaining and focus attention more on the reviewer and their entertaining takedown of a game, rather than on the game itself? There has to be a reason why no one watches shows with names like "Friendly Joe" and "The Pleasant Video Game Nerd."
Still there was something specific to this game itself, though - a hatred right out of the gate. Massive numbers of people were giving it a flat 0 on Metacritic within minutes of its release, and I'm sorry but even "Ride to Hell" and "Big Rig" and "E.T." didn't get flat zeros from critics when they were released. There was a concerted trolling campaign to bring down this game, including a lot of people on this board with only a few posts to their names and long and vicious screeds about the game and how it was the worst ever.
Why? Probably multiple reasons, but one I notice is that while BioWare has a lot of devoted fans, but it's also had a significant hate-base that does not like the progressive attitudes in its games. Gay characters, trans characters, strong female characters tend to attract hatred, and it's something as a gay gamer I really, really notice. There were a few nasty posts on the subject here, thankfully shut down, but on the larger internet it was worse. They weren't even allowed to sell the game in India because of Dorian and the other gay-positive material that they refused to censor.
It's part of the reason I react so badly to the calls to make the game more like the Witcher 3. I've watched the Witcher 3 being played, and I'm sure it's not a bad game but I've seen nothing in it that makes me want to pull away from Dragon Age 3. It's a good enough game, shiny enough graphics for this generation, and a pretty bog-standard fantasy story that seems to hit most of the clichés like stations of the cross. I suspect the love of it has to do at least partly with Gerralt, a husky action-hero voice, multiple (exclusively female) partners, and magical anti-pregnancy and anti-STD powers and who is very absolutely straight and male. No temptation whatever to romance a Dorian character, or even to have that possibility raised - there's none to romance.
There was a hatred for DA3 before anyone could honestly say they had tried it. Something big motivated that hate, and it could not have been the game itself so early on. Not that people can't like a game, or like another instalment better - after the initial hatred here, people made good and informed cases for DAO or DA2 being superior - but the rage was so absolute, so sudden, and so extreme that it did not feel like a reaction to elements in the game so much as to something the game represented.
As for the bugs, there were almost none on the PS4 that I played on. The PCers got the worst of those, and had a legitimate right to complain out of the gate, which gave me a bit of Shadenfreude. Now you all know what it was like to play Awakening on the PS3, with no mods or patches in sight - and they never fixed that 