In order to leave a Private Group from an iPhone, follow these steps:
1. Open the navigation menu in the upper left corner.
2. Select the private group.
3. Click the group options button in the upper corner.
4. Swipe to the left on your name, and select Leave Group.
5. You will be asked to confirm that you would like to leave the group. Select Leave.
6. You will receive confirmation that you are no longer a member of the group.