The answer is
just look for the now-corrected spelling mistakes, and write down the missing letters: A, P, P, L, E.
The fact that this is what we should look for is indicated by the text itself:
Once upon a time in history, (or actually a few times), some letters became red and some became green. In other places, the reds may have been forgotten forever but not here. Here almost nothing is forgotten unless it (meaning it's maker) wants it forgot.
In "history", meaning the revision history of a post. The red letters are those that have been removed, the green those that have been added. Other websites don't show revision history, but Stack Exchange does (unless the history is redacted by moderators).
So somewhere in history a word exists. It's neither here or there. Neither red or green. It's not written anywhere. If you look for it later it may be longer, I can't help it. It's part of the ideology of this place, I guess. No one can help it when others make their stuff longer.
No one can help others editing their posts, and the word we're looking for is in fact not written anywhere.
When you look for it, you may find many symbols that you didn't see before. Don't panic! they are not really greater than.
Looking in the revision history shows a trace of letters which weren't in the original post.
I wish you luck. This will require a mouse or a bit of patience.
A mouse to click on the revision history, and patience to find the right letters.
Unfortunately, the effect of this puzzle was spoiled because
you probably didn't know that edits made within 5 minutes of posting don't show up in the revision history (shadow edits, as they're called). Because I saw this post as soon as you made it, I noticed the edits right off, and also spotted you editing them out one by one. But this didn't show up in the revision history - in fact, I assumed that because you were fixing them, they weren't part of the puzzle after all. Then, after someone else made an edit, you edited the typos back in so that they showed up again, making the answer clear.