Frankly, this borders on being analogous to a classic playground scenario.
"Teacher, he won't play with meeeeeee!"
If someone doesn't want to play again, leave them be (both in person and over the internet).
Edit: This is, of course, assuming that whoever is declining does so in a polite manner.
You do it when there are (real)people around. They can't use engine there in front of you and others. In Computers they can.
@NeverBeenTimid was right to say that others can play like a GM after losing. Maybe you are right about manners and that is why lichess has added the GTG[got to go], BYE[bye], GG[good game] signs.
Many reasons I decline rematches.
1) I don't like playing more than one game in a row. I like to immediately look over the game I just played if I have time. I'd much rather do that than play another one.
2) Most of the time, to me, it seems like the reason someone wants a rematch is to get revenge because they lost. I do not think people should be taking losses personally like that, so I don't like to feed into that behavior by playing against them. It shouldn't make any difference whether their next game is against "johnny123" or "betty456" really. The most likely explanation is they can't stand the fact that "johnny123" might be sitting there thinking they are a better player, so they have to play them again to put them in their place. This often leads to:
3) Many times, I've encountered players who play so much better in their second game against me (when I won the first, often easily) that it is, quite literally, unbelievable. Fueled by this desire to get revenge, often there is a temptation to gather some help of the type one is strictly prohibited from using.
In person, if I play with someone and they ask for a rematch, I will offer to go over the game we just played with them instead, and if they don't want to do that, I will politely decline and move on. I like to play different people in person, not the same over and over.
@PhillipTheTank I also don't accept rematch as I too analyze over the game immediately.
I usually don't accept rematches, I'm not sure why but I like what Phillip said. I also just like to take a break instead of rushing into another game. Reviewing the game I just played is like taking a break and I do like to do that.
I never ask for a rematch myself, and I don't think it's rude just leaving. In person it's easy to just say "no thanks" and leave. On the internet that is what you should assume is going on if someone just doesn't accept the rematch.
On the other hand, I think many of the commentators are a little too harsh. The host puts out a well explained question that's on his mind. He doesn't deserve to be belittled or put down for it.
It's embarrassing to whine so publicly about people not wanting to play with you. Like a jilted ex-lover posting whiny drivel about their ex online. People don't want to play more than one game with you, just accept it rather than showing us all how in denial you are about that. It's not other people's fault that playing a rematch with you is evidently not attractive to your opponents.
Also, the Internet and your local chess club are different. Would you stand up at your local chess club, yell out a subject of the rant you are about to give, then give your rant? Why not, you did it here on the Internet, and the exact same behavior is clearly expected at both places.
I always accept a rematch unless I have something to do.(I usually play during my free time at work).Most of the times in the second match my opponent leave the game without resing when has a little disadvantage.That's because normally people who want a rematch after losing are very upset and frustrated, and they can't accept a second defeat just like they couldn't accept the first.What I want to say is that you are crossed that line of frustration opening a post about how bad and unpolite are those guys and expecting people in the forum will be agreed with your madness.
The usual practice in skittles rooms, at the weekly club is for spectators to challenge the table. The loser stands up and gets back in line, or goes to another table. There are no rematches when people are waiting. This is the common practice seen everywhere, which completely negates the OP's claim of rematches are most always given in club play. A rematch happens of course when no other players are available.
I'll wager 90% of the moaning is after a loss. Who's making these threads after winning a game and no rematch is made?
I almost exclusively play tournaments here. Even then, I don't like being paired with the same player multiple times in the same tournament but it happens in Arena tournaments and I live with it.
