The official Pokémon website cites two main reasons why it was banned: that it creates a strategy that frequently wins on the first turn of the game, and that it creates a non-interactive play environment where the opponent has little impact on the outcome of the match.
Due to Forest of Giant Plants, it is possible to play Shiftry very quickly, even on the first turn. When combined with cards like Devolution Spray, Super Scoop Up, and Recycle, it is possible to use its Ability Giant Fan multiple times per turn, allowing a player to win in one turn (even on the first turn).
The card is not in the current rotation of the Standard format. Even when it was part of the Standard format, it did not see much use due to the lack of Forest of Giant Plants.
This ban follows the recent ban of Lysandre's Trump Card from both major formats (Standard and Expanded) this June. Shiftry and Lysandre's Trump Card are so far the only two cards to have been banned from Expanded format since its inception in 2014.
“As of September 1, 2015, Shiftry will be banned from all sanctioned Play! Pokémon tournaments that use the Expanded format. This card has created an undesirable play environment because it:
Creates a strategy that frequently wins on the first turn of the game
Creates a non-interactive play environment where the opponent has little impact on the outcome of the match