Overwatch Game Director Jeff Kaplan took his time to talk to the players and inform them what is the reason behind the decision to postpone the Competitive Play mode. Kaplan said that Blizzard plans to bring back a newly re-designed version of Competitive Play sometime after Overwatch launches.
Here's a quote: "We worked extremely hard to get Competitive Play in the game for Closed Beta. We've been reading feedback from the community and taking it all to heart. As a result, we've temporarily disabled Competitive Play for Open Beta so that we can rework the system and make it better."
As a reminder, the Overwatch Open Beta Early Access has started. The All Access will follow, starting on May 4 (May 5) at 4:00 p.m. PDT (11:00 p.m. UTC)