Is it rude to refuse a rematch request?
Many players like to play two matches, one as white and one as black, against everyone they encounter. However, there is no rule that says you have to accept!
There are many reasons someone may not accept a rematch, such as not having enough time, or being at the end of a long string of games and being tired of playing, or perhaps, as I do, they go right into analysis after each game to look over their mistakes. I have missed many rematch requests for this reason!
If someone declines or doesn't respond to your rematch request, this doesn't mean they are being rude or 'running away.' A rematch request is just that, a request, it can be accepted, or not, and for any of the reasons listed above, or many more reasons.
If someone doesn't accept your rematch, don't worry! There are endless other opponents out there, all waiting for you at the click of that 'play' button!