If you've been looking for that LOG OUT button and still cannot find it, here's a solution for you:
READ FIRST: Logging off on Instagram (March 2016)
As of March 2016, there is no WAY you can log out of your account via the Instagram app. I'm not sure if it's a bug or if they did this on purpose. Hopefully they'll be able to fix this ASAP. You can only moderate some stuff on your account when you login through your mobile browser or desktop browser.
Logging off on Instagram
- View your profile. Click the "settings option", which you can find at the top right of the screen. Here's an example screenshot:
- Under the Account label, select the "Log Out" option and you're finished!
- So easy, right?