Are you familiar at all with who Dan White was?
If you think so, I don't see how being a leftist would have made him more or less angry that Milk stuck a home for drug addicts and homeless people, rapists and violent criminals in his district in an attempt to force out the families living there ......Seriously, look up the actual "home" that Milk pushed to have placed in Dan Whites district, it was basically hell on earth, all part of attempt to drive out the blue collar families there, so that it could be a haven for the kinds of people Harvey Milk wanted.
The breaking point, was when he resigned (stupidly), then went to get his job back, only for Harvey Milk to intervene, and prevent White from getting it.
FWIW, The police department there, wore t-shirts saying "free Dan White" as soon as he was arrested. Then again, Dan White was a cop originally.
Dan White just didn't want his neighborhood turned into a cesspool, Harvey Milk did want that neighborhood turned into a cesspool (at least temporarily), Milk also wanted someone there that he could control, and fought like holy hell to keep Dan White from even working, in any capacity, ever again......There is a reason so many families cheered when Dan White got a short sentence instead of a full term.
Dan White was a POS crazy bastard. Harvey Milk was a POS crazy bastard. Nothing more to know. This is SF after all. What more do you expect?