Based on nothing other than that "people don't really change", I would guess that pretty soon after the death of Jesus, people started misattributing quotes to him. We have recent, extremely well documented historical figures like MLK, Einstein, and Gandhi, who have quotes commonly misattributed to them all the time, that are easily disproven with a a few minutes of searching.
So, you've got an early church with a poor textual record and lots of people either making up quotes or misattributing them to Jesus, and probably kept making up new ones for decades after he died, and probably toward contradictory ends, and people get tired of it and decide to keep a list of accepted quotes from Jesus, so that people would stop making up new ones from that point on (and it doesn't appear to have worked -- the later gospels have additional quotes and stories -- in particular "He who is without sin cast the first stone" seems to have been a later addition.)
Then after that, you have this list of canonical quotes going around, and of course people want the context, because you don't necessarily know how to interpret a quote without the context in which it was said, and so you get the gospels of Mark and Luke.
So, you've got an early church with a poor textual record and lots of people either making up quotes or misattributing them to Jesus, and probably kept making up new ones for decades after he died, and probably toward contradictory ends, and people get tired of it and decide to keep a list of accepted quotes from Jesus, so that people would stop making up new ones from that point on (and it doesn't appear to have worked -- the later gospels have additional quotes and stories -- in particular "He who is without sin cast the first stone" seems to have been a later addition.)
Then after that, you have this list of canonical quotes going around, and of course people want the context, because you don't necessarily know how to interpret a quote without the context in which it was said, and so you get the gospels of Mark and Luke.