Contrary view
While it sounds like he was indeed very much in the wrong, in mitigation I will point out that in many cases when you have had a late handover and so are fast approaching an ATZ (air traffic control zone) for which you need permission to enter, and you cannot get through to ATC, it can be a pretty stressful situation in congested airspace. If you don't get the required permission in time you will need to start executing 360 degree turns in order to remain outside the boundary, which other pilots in the vicinity (and indeed any radar controller managing IFR flights in the same area) will not be expecting, so you have to keep a really good lookout and hope that you spot any conflicts.
Stress can exhibit itself in several ways - and if it was true that the controller was having semi-social chats with other pilots she knew while telling this pilot to "stand by", then I can see how that would be frustrating and induce anger in a person who is feeling stressed and (dare I say it?) perhaps in a situation that was a bit over his head and so a little frightened as well - while trying not to show it to his passengers.
It doesn't excuse his rudeness, but it might go some way to understanding why it happened.
Biting the hand that feeds IT
