What a silly topic. It seems you don't understand what is chess about. Let's assume you have played bullet or blitz game. Wait, first we need to make clear that chess is not equal game as white and black pieces. Chess is not some other online game .. hm i don't know .. backgammon? Where nobody cares when they lose single game. This is battle of the mind. It is very easy to understand when a game of chess is played for fun and when for the absolutely win. A one can read your emotions, your skills just from observing how much time and what move you make in specific position and even when you make a move, other player can 100% say with that move you are not sure or don't know what is happening or with that move you disrespect your opponent or you are not resigning in lost position. One can easily assume he is better than you and that you have won very luckily even in a way embarrasing your opponent. Bullet or Blitz game can be very agreessive. Ofcourse one is absolutely right to claim rematch and to say bad words agains you when you don't accept. And is absolutely right that person to not wish to play 2nd game. But if you did not prove in that game you are better etc. and you won very suspiciuos, and you do not want rematch and take black pieces, then sir, you are exacly what that person says you are. If you play chess for fun you can do it with unrated option.
Just no.
1) "One can easily assume he is better than you and that you have won very luckily even..."
This is an ego problem of yours. Normal people shoud not feel this way after a game of chess.
2) "Bullet or Blitz game can be very aggressive."
Any time control's game can be aggressive. Has no bearing on the subject. The fact that you take a loss personally is your problem, nobody else's.
3) "if you did not prove in that game that you are better, etc."
This is not what playing a chess game is about. Again, this exposes that most of the problem here is your own ego.
4) "and you won very suspicious"
Not sure what you are getting at here. Cheating? Winning on time (this is a completely valid way to win)? Blunder (also nothing suspicious here). My guess here is that you feel like if your opponent won when you weren't playing your best or he won on time that it is somehow suspicious and doesn't count towards showing he's better than you. Again, an ego problem. Chess isn't about being better than someone else.
5) "If you play chess for fun you can do it with unrated option."
You can also do it with the rated option. You don't get to decide this. Most people enjoy the game more with ratings.
In summary, this is entirely a "you" problem. Most people can just play a chess game and not have their ego crushed or manhood questioned or whatever you are introducing.
I almost never accept rematches because 1) I don't like encouraging the ego thing--subsequent games are almost always more contentious, opponent behavior gets worse, etc. 2) along the same lines, a lot of times "revenge" is so important to my opponent that his play becomes let's just say a lot more precise in the next game(s). With so much ego involved, the temptation rises for them either way, and I'm just not interested in fueling that.
Tip: don't take games so personally, just play somebody else. You may think your opponent is chugging beers and high-fiving a room full of his bros after beating you, smug in the knowledge that he is your superior now, but aside from the chessbrahs twitch stream, this is very rare, and should be pretty irrelevant to you even if it was happening if you are not really insecure.
I don't know if I would go so far to call people immature or morons simply because they want to play an rematch. I think games should be the best out of three as this gives both people a chance to play with both colors, as some people are better with white than they are with black and vice versa. Some people will let the server abort the game if they start a game with black color, so stop with the name calling and be understanding about the advantages and disadvantage in chess!
You do understand that 1 and 3 are both odd numbers right? if you play best out of 1 or best out of 3, one player will still have white more than the other player.