Kevin Durant leaving the Warriors, opened up the Larry O' race, and him leaving wasn't such a big surprise. There were numerous reports that Durant was eyeing New York and that he was frustrated after winning to titles and two Finals MVP's he still wasn't considered to be the best player in the NBA.
The blow-up with Draymond didn't help, and it revealed a tension within the Warriors locker room. Steph, Klay, and Draymond changed thair game to accommodate KD, the team did everything they could to make him happy, and it obviously wasn't enough. KD later explained he never felt as "one of the guys" compared to the Warriors trio as he wasn't drafted there. This era of Golden State Warriors will always be Steph's team, Klay will always be the weird/cool brother, and Draymond will always be the annoying one who stepped up when it's most needed and brings out the warrior in everyone.
It is more likely KD didn't feel that the fans loved him as much as they did the trio and that he had to leave to be "the guy." From the fake Twitter account to his many clashes with the media, Durant obviously needs a lot of outside confirmation and love. That is something the Warriors could never give him. But, him saying he "wasn't a part of the team" hurt Draymond (via Woj Pod):
"The thing that bothered me the most was that when Kevin goes [in the media] and says ‘I wasn’t a part of [them]’ or ‘I was different from those guys’. A part of it is like, no you were one of us, and it pisses me off [that you would say otherwise]. ... So like, the thing that bothered me most was, I lost his trust, and how do I get that back?"
For most of the episode, Draymond accepted responsibility for his blow up on the court and that he apologized to Durant when he realized how much that situation hurt him. He obviously cares about KD a lot and wishes he did better to let him know how appreciated he was in Golden State.
The only problem is, even at their best the team probably couldn't give him what he's looking for.