One reason I can think of for some leaving is their stats are being negatively affected. They want a game where they're doing well and thus improving their stats.
Such behavior is the epitome of selfishness and those who do so are not team players.
So as far as I'm concerned good riddance to those who behave that way. They don't belong in any team oriented activity. And the Crucible is not 1v1. It's a team based game mode.
There are of course many other reasons. Some simply don't like losing. It's not fun. But that's reality. You win some and you lose some. And sometimes things come up where one has to leave for a variety of reasons in which case it's understandable. But that's not what I'm referring to.
Although that may come across as being harsh to some, it's the truth.
English
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Bungie made the game this way, stats matter. Players will protect their stats and leave. It's a bad culture Bungie fostered.