I'm going to prefix this by saying I actually know a. bugger all about sports, and b. a fair few American football fans here in the UK. As in, proper fans. A good friend of mine played American football locally for a few years - might still do, not heard from him as much lately.
So, with the preface that not only am I completely ignorant to this entire subculture but I'm trying to argue a rule that I've met living exceptions to - I think a huge part of it is the fact that it's got the word "American" in front of it. And the other huge part is that it's used the word "football" to describe something that, in the minds of a good majority of the planet's population, definitely isn't.
Real football, as people in every other country consider it, is one of the most beloved sports worldwide. Calling your sport American football sets it up as a direct opposition. A counter-argument. "Here's what we're going to do instead." The two sports needn't be mutually exclusive, but by insisting on calling it football, it feels like someone's looked at soccer and gone, "You can keep that bullshit with the sphere - we're going to don some armor and carry an egg."
On top of that, the word American is in itself a big sign that says "This isn't yours." When people follow a sport, they like to feel involved. They like to support their local team, feel like they're on the journey with their heroes. Very few people are going to feel personally involved with a sport that has a foreign country's name in front of it. Who's heard of the "English American Football Team?" I presume it does exist, and I presume it's got fans, but even just as a phrase, English American Football Team is, semantically speaking, nonsense. Giving a sport a particular geography limits its breadth innately. It's a psychological barrier. A big mental wall that, again, implies "The rest of you are not part of this."
If you started calling soccer football, and came up with a new name for American football, I think a lot of people would feel a lot more like it was a game they could be involved in. Because while there are fans worldwide, it's not really a global sport, and with a name like that I don't know if it ever can be. Hell of an image problem if you ask me. Which you didn't.