I have a confession to make.
The truth about "emo" is that most of what is accepted here isnt really emo, it's some form of indie rock. People here point back to Cap'n Jazz and Sunny Day Real Estate as the progenitors of everything they listen to today, which is true, but they are not progenitors of emo. They are pioneers in college indie rock (and in SDRE's case, mainstream indie rock [yeah, they were on MTV in 96 and half the members went to Foo Fighters, look it up]) incorporating influence from post-hardcore and emo.
There's a reason this stuff is called "post-emo indie rock," or as it has been branded thanks to a handful of early 90s bands no one remembers any more who were from the actual midwestern United States and actually played emo (including Gauge, Current, Ordination of Aaron, Endpoint, Split Lip, Friction, and Chino Horde), "Midwest emo." The reason is because it isn't really emo and needs to be distinguished, kind of how 'metalcore' came about when that scene stopped being primarily hardcore and moved to metal/alternative.
In a similar sense, the post-emo/midwest/indiecore scene moved away from hardcore in the mid 90s, and was seen as a new, post-emo movement, hence the name and ridicule from hardcore bands. Meanwhile, I doubt anyone who lists Mineral or American Football as their favorite 90s "emo" bands could name any actual mid/late 90s emo. Sucks cause there's so much good shit: Traluma, Chocolate Kiss, Stratego, Edaline, Twelve Hour Turn, Unionsuit, Blue Water Boy, Still Life, Thumbnail, Four Hundred Years, Assfactor 4, Sleepytime Trio, Amber Inn, The Deadwood Divine, Bread and Circuits, The Red Scare, Metroschifter, Radio Flyer, The Hal Al-Shedad...I could go on.
You see, the fake/real emo dichotomy is nowhere near nuanced enough to capture the layers of relation to emo that all the music referred to as "emo" has. That's a pretty annoyingly confusing sentence so lemme break it down - there are four types of emo: