Because to them, stats mean more than skill. Therefore, once you lose stat advantages, you lack the ability to win by any means other than an lucky break where the opponents make a mistake or stalling out the game to the point that you could have won 2 more games in the time it took to finish winning that one, or both.
Also, most people give more of a damn about their personal stats than they should. If they win by going 12/14/5, that looks bad, or at least not great, on paper for themselves personally so they just refuse to let it get to that point. Basically, they'd rather quit the instant they fall behind so the number of deaths assigned to their name is minimized whilst also maximizing the number of kills they get from good games at the same time. In this respect, this game is becoming more and more like FPS games where "if I lose its not my fault. My stats prove it, see??"
Its also worth noting that they might want S ranks, or that a game lasting 60 minutes won't give you 3 times as much IP or LP, so either winning or losing games quickly is more beneficial to you than dragging out just one game.
It really matters on your own point of view, really.