What you're describing is someone trying to manipulate you and put pressure on you to obey them because they sense that after slipping up in the second game you could be a source of cheap points for them.
In general, if I win or lose I rarely accept rematches. If I've just won, there's a highly increased chance that they will try to get their revenge by beating me on time. Generally therefore I usually only accept rematches if I respect the way my opponent played. If they played a good game, slipped up and I won, they're less likely to play zer0-chess just to win on time in the second game. If they played badly in the first game and want a rematch, they are probably going to attempt to win on time and there's no need to accept a rematch. You slipping up and losing was a sign you could have been getting tired and it's a good idea to take a break at such a time.
It is unethical to come on the forums and whine about the fact that others won't accept a rematch. When paired with you for a rated game, they are under ONE AND ONLY ONE OBLIGATION - to complete THAT GAME AND NO MORE! Nobody is required to give you a rematch!