Destiny has no private matches at all. Proof provided by this youtube video above, go to 1:15:00 he says private matches aren't in the game and there aren't clan battles either.
This company would be literally stupid to not add this.
How will clans work without custom games?
How will friends play against eachother?
How will any tournament exist?
How will people train for matchmaking?
How will 1v1s be possible?
Honestly without custom games this game is pretty dead, there will be no competitive scene at all because there won't be any chances to prove it. I've played Halo for years to know that custom games are something I do every day and is very important. While this isn't Halo, it's important.
Desired custom game options: http://www.bungie.net/en/Forum/Post/68034408/0/0
Edit: Stop attacking a straw man and don't put words in my mouth based on what you assume. I bring up valid points. While you may not want a competitive scene in Destiny, it should be there. I don't think Bungie hired a competitive lead and said they would take steps towards making competitive gameplay for nothing. There is a ridiculous amount of narcissistic replies saying how they're thankful they don't have to deal with "competitive players" ruining their game. This is so pathetic.
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A lot of people will be unhappy with the amount of pub-stomping there will be in matchmaking from organised clans that would otherwise be engaged with each other in customs. Playing solo or even with a friend could prove to be a real pain for some people without the ability/desire to form a 6 man squad for Crucible. Eventually the rage caused by this will reach boiling point on the forums and unranked custom games will be introduced to alleviate the pressure, and soak up the tears. < you heard it here first people ;)