I could stand losing to AG or DP-era Ash, but no more than that. I'd especially hate losing to his BW self.
Barry... I wouldn't like losing to either since he's pretty damn shallow, though it wouldn't be the end of the world for me like it would for most other options I picked. If I lost to Barry, I'd chalk it up to dumb luck on his end since I can see Barry being the kind of guy who would have dumb luck every now and then to win a battle.
Trip, though, no. Just... no. He's roughly as shallow as Barry without being interesting or endearing to make up for it, and for all the times the show TRIED to hype Trip up, it was only when he did things that ANY newbie trainer would do - namely relying almost solely on his starter and making said starter severely unbalanced. I would quite enjoy pitting his Serperior against my Ferrothorn and watch Trip cry as his Serperior's moves do jack shit against my tank and its speediness only serving to quicken its own demise when my Ferrothorn Gyro Balls that motherfucker. So yeah, losing to Trip would be unacceptable. I mean hell, who'd want to lose against a dork who got LAST PLACE in the Unova League? :P
I really wouldn't like losing to Iris either, since the vast majority of Iris' victories were cheap bullshit owed largely to Lady Luck favoring her. Iris herself, for all the hype she's gotten bestowed upon as a trainer, has really not been shown to be all that special when she actually battles since most of her victories are won by purely overpowering the opponent with little to no thought or strategy implemented to seal the deal. I feel bad enough for the victims of Iris' lucky streak; I'd feel much worse if I somehow got screwed over in a battle because her Axew learned Draco Meteor or something out of nowhere to instantly win, or because her Dragonite is virtually untouchable even to types of moves it should be critically vulnerable against.
And Team Rocket... for obvious reasons. If I lost to Team Rocket I think that would be a sign from the universe telling me to give up being a trainer immediately before I humiliate myself even worse.
Wouldn't like losing to Misty either; none of her Pokemon particularly impressed me and logically she should be impossible to NOT beat if I had the perfect anti-water team set up. Unless this was set in Best Wishes, in which case I'd have to pack a team of Rock, Ground, and Fire-types to stand a chance against her.
For others, I'd obviously hate to lose to Cameron, especially if I lost the same way Ash did. Because then I would definitely have to jump off a cliff, for I would be incapable of living down such a stupid loss. I wouldn't like losing to Kenny either, because he sucks and my Breloom would kick his Breloom's ass. Hm, can't think of anyone else at the moment that I would be pissed at losing to.