It would be better if people rated themselves, because as it is the ratings tell very little about each players skill. So much depends on which opponents you have had recently, and your level may move dramatically up and down, while ones skill actually remains more or less the same.
It would in my view also be an advantage, if the opponent were chosen randomly within each players (self chosen) skill level. There could then be an additional "statistcs" column showing the percentagewise ratio between lost and won games, indicating to the player, whether he or she should remain at the chosen level or move up or down in order to achieve the best chance of an even game (aiming at a 50-50 percent distribution of won and lost games respectively.