Because they respect their opponents, the game, and have integrity.
Why do master chess players resign when they're about to lose?
Besides knowing that their opponent is very unlikely to throw away a winning advantage, "premature" resignations in slow games allow players to save energy, as many of them work on chess after a game (while staying at a hotel, for instance). Why waste energy defending a lost position for one hour, when you could review your game and see what went wrong?

Yeah.... I had this match at Jr. High Nationals last year in the last round where my opponent just sat there and waited for about 30 minutes, waiting for his time to run out. I finally told him:
" I am sorry to be rude, but I have a schedule to keep, so can you please resign or make your move?" (It was a mate in one.) He also offered a draw!
Wow. That really sucks. What a loser. I can't imagine what its like to be in your position, but I'd be tempted to pull out a novel and start reading it. You could pull out a chess book, but then that might be against the rules or something.
You could just sit there and stare at him. Just stare for 15 minutes. Or maybe say something like "I'm sorry but I find you very attractive. While you are staring at utter defeat here, I'll just be undressing you with me eyes. " OR look at how much time is on your clock and go grab a burger. Be sure to be back before your time runs out. That way the moron might abandon punishing you for winning and walk away. haha.
There have to be 100 other ways to screw with a guy like that.
that is nasty, i agree what a looser.

Grandmasters resign because they don't want to waste time, or maybe because they hate to lose. Personally, I hate when players resign because it is always fun to checkmate someone, but saving time is gratefully appreciated.

Masters do that
But mortals like us should avoid resignation as much as possible unless the mate is staring you or you are in an elementary mating ending.There is so much to be learned from these inferior positions
Well said

Had one this week and the opponent was way ahead but missed the Checkmate twice in a row with the Queen, so I figured he/she was rusty and so I let him/her screw it up into Stalemate.
Tough love but we have all been there. In this case I am confident they will have gone and worked out NOT to do this again.
You might be miles ahead but ya gotta finish the job professionally because next time it might not be so simple/obvious.
I do normally resign but in this case for me it was clear they were messing up their endgames.

If you play on in a dead lost position, you are basically telling your opponent "I think it's possible that you're going to screw this up." Telling a super grandmaster that you think they might screw it up is widely considered a slap in the face. It's like telling a teenager that you think there's a chance that they might not be able to tie their shoelaces.

I think GMs resign because.. I mean come on! They are full blown GMs losing! They probably studied chess so much. And they lose? That has got to be humiliating. Lets say you were a GM. You were... 3150 Elo. Wouldn't it be embarrassing if you lost to a … 1500? You wouldn't rage quit before he can ladder mate you? Plus, keep in mind that losing to that low Elo player at yours would lower your Elo dramatically. This comment approached from a GMs POV.

Whatever your rating you resign when you consider the win trivial.
I understand if my opponent doesn’t resign when he’s down a queen for a piece, people often get too nervous/excited when they’re dead winning and fall to a sneaky trap by their opponent. But, if the players are rated 2000+ then they tend not to counterblunder much and resignation is the best thing.
I defeated an IM in an OTB game once. He blundered a Knight on like a 5 move tactic, but I had a slightly better position before that IMO. However, he played on for about 10 tedious moves before he resigned. My guess is because I am only an expert. In masters games, my guess is they resign to each other because the level of play is very high. In other words, respect.