I don't have time to watch your youtube, however it's not really a myth, just no longer true. There was definitely a long period of time when it was kind of true. I say kind of because it's specifically a diocesan cathedral.
While it's hard to make definitive statements about when a lot of cities originally became cities, it was first formalised in the 16th century, and at that time all the cities were cathedral towns (or more accurately, they were diocesan cathedrals meaning that churches in other towns in that diocese were administered by that cathedral), and significantly in many cases these cities were smaller than other towns in the diocese. The important part was that these particular towns with cathedrals that had always been called cities for as long as anyone remembered were recognised as cities by the Crown, and other towns were not allowed that status. Later on, Henry VIII created new dioceses and granted those towns (and they also all happened to have cathedrals) city status as well. So, at that time at least, there was a strong precedent that city status and being a diocesan cathedral town were linked, and in fact people were told that cities were cities because of this, even though technically towns became cities only by Royal decree and dioceses were only created by separate Royal decree, but historically both were done at the same time.
This understanding was only really challenged in the early 19th century, when some more towns with cathedrals became new dioceses and their local governments assumed they were now cities and renamed themselves as such. Clearly, the Crown wasn't too worried about this as it took nearly two decades for this to be noticed (and only happened in the context of a Royal visit to one of the cities), at which point there was an act of parliament specifically to confer city status on these new large towns that were already calling themselves cities, again reinforcing the people's understanding that towns with diocesan cathedrals should be called cities.
The interesting stuff happened at the end of the 19th century, when some of the other new diocesan towns that were quite small decided the also wanted the prestige of being a city, but were told they were too small to justify it and rightly complained that other cities were even smaller, but they weren't going to be downgraded to towns because they had always been called cities as long as anyone knew. And then Birmingham, the third largest town/city in the country petitioned to be a city on the basis of its important, and was recognised, at which point the link between city and cathedral was broken down. After that, a few more large towns also successfully petitioned for city status based on size or historical importance.
It can be said that the link between city status and cathedrals was firmly broken in 1974, when all existing cities lost their city status, and towns had to apply for city status along with justifications. This was re-granted to all the existing cities (actually, I've got a vague recollection that at least one didn't bother and lost its city status), and at the same time city boundaries were redefined to include the metropolitan areas that would previously have been considered towns or villages in their own right.
So, in one sense the assertion that towns with cathedrals are cities isn't quite true, and is definitely wrong now, but about hundreds of years this was actually the case. Arguably, correlation doesn't imply causation, but the Crown seemingly made an effort for a long time to ensure that the correlation held to ensure the set of cities was exactly identical to the set of diocesan cathedral towns. So, it's also not a myth.
> the video I've posted goes into great detail, but you'd know that if you had watched it.
Firstly, I'm sure you could have worked out that "your youtube" was shorthand for "the youtube video that you linked to". Had you even mentioned that it was a Map Men video, I might even have decided to watch it even though I was short on time at the time, but as it was, I just had 5-10 minutes spare before I had something else I needed to do so I didn't even click on it. But even if I had clicked on it, I wouldn't have had time to watch it at the time.
Anyway, I finally found the time to watch it (somehow I missed it even though I've been subscribed to the channel a long time), and it basically agrees with all the points I made, but in a much more interesting way and with additional information. I'm not sure that the tone "you'd know that if you had watched it" was really required, given that nothing that I'd written was contradicted by it, and I didn't really learn anything significant from it that I would have added to my post.
So really, the only thing you're arguing about is the definition of myth. And to me something that used to be true but now isn't doesn't qualify it as a myth [1] [2]. I said exactly that in my post. You'll notice if you re-watched the video you posted, that they also don't ever call it a myth, they say that it is wrong, and later clarify that it used to be true: "So why then do so many people think it's about cathedrals? Because it used to be."
> It is a myth that the former definition of what counts as a "city" still applies to this day, yes.
So no, it's still not a myth, it's just incorrect.
[1] For example "carrots make you see better in the dark" is a myth because it is wildly held, is wrong and has never been correct. Likewise, "the moon is made of cheese". However, "Trump is the president of the USA" is not a myth - it was once correct, but now isn't as he's now just "a president of the USA". Someone in 1920 who'd missed the recent news and said "Women are not allowed to vote in the UK" wouldn't have been repeating a myth, just saying something that was factually incorrect.
[2] I checked a number of dictionaries to make sure before writing this, and while most support a meaning like "a widely held but false belief or idea" when you delve into that in more detail, most dictionaries seem to have the view that a myth has no actual basis in fact, so something having previously been true and now no longer true doesn't seem to fall into the myth category.
