Mistake 1: Talk about gun homicide, but not all homicideThe first mistake that I noticed was in their Myth #2 (also present in #7). In the fact check, they cite gun-homicide statistics. Okay, fine. Not really a surprise that more guns is connected to higher gun homicide and gun murder. The problem is that gun murders shouldn't be the specific concern, murders generally should be. While it is certainly true that gun homicides get rarer if guns are rarer, that does not imply that the overall rate of homicide will go down.
In Myth #7, they note that women in states with higher gun ownership are more likely to be murdered by a gun, but the straight comparison of murder rates is not presented. If they want to make the honest case for gun control, they would need to demonstrate that reduction in gun availability lowered the rate at which women were murdered overall. Removing guns would not help if all the people were stabbed to death instead of shot to death.
Mistake 2: Mass shootings stopped by good guys with guns...
In Myth #4, they talk about armed civilians stopping. Mass shootings that end before the third victim are not mass shootings, and so don't get counted. Basically, they are stating that once a shooting became a mass shooting, armed civilians didn't rush in to stop the shooter. Fine. But an armed civilian who stops a shooting before the shooter hits three people prevents it from counting as a mass shooting.
Basically, the good armed civilian is in a no-win situation here. If they stop the shooter before they kill at least three people, then they didn't stop a mass shooting because there was no mass shooting. But if they let three people get hit then they didn't stop a mass shooting, they just ended it a little early. It is still a mass shooting.
Mistake 3: Self defense with a gun = killing someoneThis mistake spans two of the myths (#5 and #6). They talk about the rates of people using firearms for self-defense, but do it in only in terms of shooting people. The only self-defense uses that they count for these statistics are cases where the gun is fired. A gun doesn't need to be fired to be used in self defense. The exact numbers are murky, but the estimates of defensive uses of firearms would put them somewhere above the gun death rate overall.
When talking about the defensive use of firearms, it is very important not to assume that all defensive use ends with the death of the attacker, especially since (I would hope) that killing the attacker is not the primary goal. Eliminating the threat is the goal, whether this ends in the death of the assailant or not. If the attacker runs away, that is still mission accomplished.
Some of the points in the article are interesting food for thought, like myth #3 about an armed society being a polite society, and some points about the loopholes are interesting, and might merit some discussion. I can't trust that it is honestly presented though, since they aren't willing to present honest arguments about reducing violence generally (which has been trending down, as one of their sources notes). If they want to attempt to convince me that additional laws will help reduce violence, they need to show that violence on the whole will actually be reduced, not just gun-related violence.