From what I believe...
Sonic '06 was when it all started. Sonic Team released a bad Sonic game and it took them years to recover.
During that era, "gamers" preferred popular games like Grand Theft Auto: San Andres. Call of Duty: Black Ops or Red Dead Redemption. Games that are regarded "grown up" or sophisticated while those "gamers" regard Sonic fans as children or "autistic" for liking something colourful and outdated.
Meanwhile, Nintendo made their own colourful and childish games, and even pro-gamers thought Nintendo were pooping gold. It was unfashionable to hate Nintendo but it was to hate Sega.
There was also a streak of poor marketing that didn't help.
Sonic Adventure and Sonic Adventure 2 were re-released, but were criticized and never regarded as good to begin with reviews that tarnished the reputation of these games desite having favourable reviews during the Dreamcast. This was because these reviews were for the 2010 and 2012 re-releases, which were buggy for being rushed ports to PC and platforms at the time. But because of the harsh judgement of the re-releases, this made everyone thought the Adventure games were always bad.
IGN gave unfavourable reviews to Sonic games, even showing footage where they purposely played the game poorly just to make their games look bad.
In 2013-14, Nintendo and Sega had a partnership to release three exclusive games for the Wii U. Those games were Mario & Sonic at the Sochi 2014 Olympic Winter Games, Sonic Lost World and Sonic Boom: Rise of Lyric. Whenever Nintendo were breathing down Sega's neck during the development of Lost World or Sega was just brown-nosing Nintendo, Sonic Lost World is regarded the least-like Sonic game. With fans being more favourable of Mario & Sonic Olympics and Sonic Boom: rise of Lyric being so bad, it's compared to Sonic '06. Nintendo, instead of claiming their share of criticism of the bad games that were made under their partnership or refusal to help with the development of Rise of Lyric, pretty much threw Sega under the bus. Everyone just rolled their eyes at Sega and chalked it up to another bad game from them, while Nintendo remained blameless.
I believe the tipping point was IGN's Game Scoop!, where they doubled down on Sonic. They were hating Sonic so much that it was obvious they were doing it out of the trend to hate Sonic and appealing to the audience than any legitimate reason. Ironically, this was when Sonic was successfully recovering his reputation with games such as sonic Generations and Mania and this was a huge wake-up call to the fact people were hating Sonic more ironically than people loving Sonic unironically. So their IGNorance helped break the on-going hate for Sonic at the time.