To be honest though, the Atari 2600 and the Atari 5200 do not belong in the same generation. And, at the time of the 5200's release, it was not considered a 3rd generation console. Advertising for the 5200 and Coleco's Colecovision clearly pronounced them as the first "Third Generation" systems. I'm not sure exactly at what point someone decided to retroactively downgrade them in history. But, it's probably because the North American Video Game Crash of 1983 was used to delineate the 82'-84' systems from the rise of the NES since they never directly competed with each other.
Note this 1982 article from Electronic Games Magazine, whose title reads, "Third Wave Video Gaming Comes to Market" (referencing the ColecoVision and the 5200 as the start of the 3rd Generation):
Here's a comparison of Pac-Man on 2600 compared to the 5200 and Coleco Vision:
Here's Nintendo's Donkey Kong on the 2600 compared to the ColecoVision:
This general consensus (which is blatantly wrong) is used as justification for the currently wrong consensus that Switch is eighth gen. "It has happened before that a console manufacturer has had two consoles in the same generation." Except it didn't. History was revised because the general consensus is arrived at by the gaming community, and the gaming community plays console wars. A generation without a winner doesn't fit the big picture and the actual third generation didn't have any winner. So the fourth generation NES became third generation while the third generation became a footnote of the second generation.
Other reasons for labeling Switch as eighth generation were based on mainly two big assumptions:
1. Switch is a Nintendo console, therefore it will have a short lifecycle, approximately replaced in 2021.
2. PS and Xbox consoles have much longer lifecycles, so the PS5 and Xbox 4 shouldn't be expected before 2021.
Put these two together and you run the risk of misalignment of generations, because the Switch successor would be 10th gen if Switch is gen 9 while the PS5 and Xbox 4 would be 9th gen. The generational model devised by the gaming community would be off by a full generation, so Switch had to be gen 8 to prevent that from happening. That's how it got put on Wikipedia that way. For those who don't know (apparently there are quite a few people here), Wikipedia is a user-generated website, so just about anyone can upload and edit articles.
But in the year 2020 it should be clear that both assumptions above were terribly wrong (expected, because the length of lifecycle theories were wrong to begin with). There's no risk of misalignment of generations anymore. Launches of consoles that belong into the same gen being spread out over three years is nothing odd in video game history, and with generations getting longer nowadays, Switch falls well within the acceptable range anyway.
One constant oddity in the generational debate has been the Dreamcast's classification as gen 6. Those who insist that Switch is gen 8 should also consider the Dreamcast gen 5, because pretty much everything they throw at Switch applies to the Dreamcast in more severe form. But over the course of the last three years, I've not seen a single guy who would put the Dreamcast into gen 5.
In any case, as time passes, things will get more interesting. If Switch continues to be put into gen 8, then Nintendo will eventually be the first company to undo a ~60m headstart of a competitor and Sony will be the shameful company who pissed away such a huge headstart. In that case, history will remember the PS4 as a loser.