I think he's just not up-to-date on what Twitch would consider a 'hateful slur'. Think of all the fucked up, weird, schizo's in the dead categories on Twitch. Look at the fucking 'Deer Girl'. Calling someone mentally ill is absolutely 'Hateful Speech' in Twitch's book of Grudges. And that's basically all he's done for the past four years. Every single time he gets someone in his crosshairs he resorts directly to calling them mentally ill sociopath. You can absolutely see why Twitch's legal team would decide to distance and disassociate themselves from a 'problematic' content creator.
Also, remember, he was never banned. He's basically had Twitch take back their endorsement of him. Not a big deal, at all, but Dave realizes just how much money he gets from gifted subs/bits and he's extremely pissy about how many people flat-out refused to transition to direct tipping.
The switch to YouTube is literally just to save his ego. He has to be the one getting the final say or the last laugh. It has to be his choice to tell Twitch to go fuck themselves, otherwise, he looks like a beaten dog whimpering next to Twitch's table for some scraps. (In his mind, at least)
On an unrelated note, how badly do you guys think Dave would struggle if he was forced to play a Total War game or Europa Universalis IV/Stellaris/Endless Space (1 or 2)? I'm asking because I just recently lost a 260~ turn game of TW: Warhammer 2 and it damn near broke my heart thinking of all the hours I burned just to get my teeth kicked in.