Earlier quoted context omitted.
LTE's initial iterations were actually not considered 4G by definition. Part of the longterm evolution part was that as the components were upgraded they would comply with 4G. I can break 100mbps down in a few places on an iphone SE with only a cat3 modem, but that's pushing the spec's real-world limit for that. Today these speeds are easily achievable on most networks, it's just unlikely for AT&T due to congestion a…
I was about to say that it was mostly Sprint and (again) AT&T advertising 3G as 4G, and for example Verizon had real 4G from the start. But now as I think, I remember that Verizon had 4G that was capped to about 1mbps in certain areas and then gradually speed increased per area.
Since the ITU had declared that Sprint's WiMAX network and Verizon's LTE network weren't real 4G, T-Mobile decided that they could call their (just-as-fast-as-early-LTE-networks) HSPA+ network 4G too, and then AT&T was almost forced to follow suit because T-Mobile was advertising how their 4G network was so much bigger than everyone else's.