Only the ill-bred fail to understand that when asked for a rematch granting at least one is good sportsmanship and good manners. Of course if circumstances obviate engaging in a rematch, then it is not expected. In over-the-board casual chess around the world, granting a rematch is a social norm. Try hanging out at a chess-playing venue and refusing rematch requests. You will soon be known as a jerk and find it hard to get anyone to play with you. I do not think that the anonymity of online chess changes matters.
You are comparing oranges to apples. Casual chess is unrated. Most of games here are rated and should be compared to competitive chess. Have you ever played in an official chess competition? Then you should understand how stupid a rematch request would be. Imagine Naka asking Magnus after a loss: "Hey, let's play another one. We still have enough time before the next round".
Rematch option in online chess is just a convenient way to keep playing against the same opponent when both want it.
Oceanoptic replied:
Not comparing apples to oranges. A chess.com-rated game is hardly as serious as a FIDE-rated tournament with an entry fee and cash prizes. For me, blitzing on chess.com is casual chess. I should have said that refusing a single rematch after winning the first game is ungracious and poor sportsmanship. At any chess-playing hangout always refusing a rematch after winning the first game with an opponent will, I assure you, make you quite unpopular. If you grant a rematch and win it, I see no obligation to grant another.
I don't believe is bad to decline a rematch, specially doing it if you are not planning to play another game.
I usually deny a rematch if I am not planning to play another game.