Usually people don't say anything, so if I play blitz, which is not very often, I just click on a new game whenever I'm done. I don't mind if I get paired with the same person, but I don't necessarily invest the time to see if someone wants a rematch, since the common courtesies are often not reciprocated. Even in a game that takes days some people don't say anything! Is that rude by normal standards? Kind of, but I don't let it bother me. If they play, they play, and if they have their reasons not to chat, I don't question that.
Chess Players Are Soft

SOME PEOPLE NEVER REMATCH, IT IS A LIKE A LAW THEY CREATE.
MY COUSIN tenlong says...."I NEVE REMATCH" haha he is just having fun
What is the point in a rematch? This is the internet. I don't know the person I'm playing against, so there is no reason I would want to play a game against the same opponent over anybody else.
The only thing accomplished by a rematch is building up feelings of hostility toward your opponent. Say a person beats me three times, and offers rematch-after-rematch. What am I to speculate about their motives? "Oh, this guy is such a weak player, I'll use him to build up some rating points". And then after I win a game, the rematch requests suddenly stop, showing that my speculation was probably accurate, and that their rematch requests were based on disrespect.
For reasons like this, I don't accept rematches after I lose. If the losing player offers the rematch, the circumstances are different and I don't have as much of an issue with it. But in general I don't like to give feelings of tension and hostility a chance to develop over the course of several games, when simply finding a new opponent has all of the pros and none of the cons of rematches.

Yeah, I don't like playing soft chess players either. This is why I rarely play chess against my dog or my cat.
Seriously, though, you do know people have lives outside of the internet, right? Maybe your opponent only has time for one game, or two. Maybe he/she fired up the phone for a little bit of chess while on the subway going to work, or on the toilet, and now has to go. I really doubt many people care about their "ELO", i.e. fake and meaningless chess.com rating that has nothing to do with ELO.

Is the average chess player soft and scared of a competitive game?
You, and others, may, or may not find this offensive. No one is here to feed your ego. Most are here to...Oh i dont know...play chess. If youre into rematches, then play a chess engine. I like Frank Marshalls quote as to why he preferred tournaments over matches. He said something along the lines of: He preferred new names, new faces, new sights.
I can't believe some of the idiots on this sites. Because some people don't want a rematch most of chess.com is soft?

If youre more concerned about online points, and humiliation, youre into chess for the wrong reasons.
I think if the losing player challenges the winner to a rematch, the sporting thing to do is to accept and give them a shot at revenge, and I always try to do so. That said, you can't really know over the internet - maybe your opponent doesn't have time to play again. Best not to read too much into it. Chess games are emotional enough without imagining all sorts of ill-intent that probably isn't there.
Is the average chess player soft and scared of a competitive game?