Who does most of the "fact checking"? The mainstream media. And what are the vast majority of the members of the MSM? They are liberal. As a group, they are biased, they lean left. Check out the Allsides bias chart at the link provided. Note that one of my most preferred web sites, realclearpolitics.con, is right in the middle. Meanwhile, check out where the biggest media brands, the "most trusted" organizations, the most listened to/watched outfits are-CNN, AP, NYT, Snopes, WaPo, NPR, USA Today......all on the left. They will twist the interpretation to fit the preferred narrative.
Allsides also has a good article about 6 ways that fact checkers are biased, link is below. Very interesting, and generally supports things I have observed from the "fact checkers" over the years. In addition to their 6 identified methods, another one I have seen used vs Trump to pile on the total number of "lies" from him is to take a statement from him that is clearly an opinion and label it as a lie. Obviously a poor methodology. One big example of fact checking bias is how they called the claim false that Obamacare would cause people to lose their doctor. Of course, when it actually started happening Obama was awarded the "Lie of the Year" for saying that people would NOT lost their doctors.
I did a search on "Biggest fact checker mistakes" and there was a big list, of course. So for kicks I decided to go to the one from everyone's favorite source, Fox News, since I hadn't been to their site for a while. Of course, if the thought of going to that site for information makes you nauseous, the list of responses includes ABC, CBS, The Telegraph, and others.
https://www.allsides.com/media-bias/fact-check-bias-chart
https://www.allsides.com/blog/6-ways-fact-checkers-are-biased
2021 marked another year of brazenly slanted media coverage, and the "fact-checking," industry, who've long cast themselves as impartial arbiters of truth, was no exception.
www.foxnews.com