Update! Overwatch team has come out and said they made a mistake and that competitive mode will release as planned in June. Original article found below...
The last we heard of Overwatch's competitive play, it was that the feature would not be launching with the game, and would be added "sometime in June". VG247 points out this morning, that this date seems to have been pushed back. The info comes from the game's official Twitter, which slates the mode for mid to late July...
@adrianmaturell We'll be introducing our Competitive Play (hopefully) later in July. Stay tuned!
— Overwatch (@PlayOverwatch) May 27, 2016
A second tweet further confirmed a release window of mid to late July. Unless you were playing a TON of Overwatch during the beta, you likely didn't rank high enough to even unlock the game's competitive mode. The mode allowed players to receive a "tier" ranking after a qualifying match to better rank them with teams. Obviously there's a large community who wants a more competitive element to this game, so let's hope they are taking this additional time to get it right!