Harriman, on screen, is a mystery as to how he became captain in the first place.
I think the idea was that he was SERIOUSLY intimidated by the presence of Captain Kirk, Scotty, and Chekov. Since these are men who saved THE UNIVERSE *multiple times* and we rarely see them given the proper respect for it (the TNG episode "Relics" was just out and out disgraceful), I didn't mind seeing some awe there.
On top of that, Harriman had to be aware that two previous captains of ships called Enterprise (Decker and Spock) had relinquished command to Kirk on what ended up being a permanent basis for one reason or another - both of which amounted to death, really. (Yeah, I know, Decker didn't DIE, but he also no longer exists as Will Decker.) So, that doesn't help instill confidence.
AND, there were all those reporters and cameras. Starfleet trains for things like the Kobayashi Maru - I'm not sure how much training they get for press junkets and addressing large groups that aren't under one's command.