If Instagram makes it a hard time to login to and/or verify accounts with a redirect back to the login page, this happens due to a recent update that made verify procedures tried from a browser, not always possible. Also, even some IG app versions continue to have this glitch, so keep reading for the solutions..
These loops mostly happens if you are using a desktop or mobile browser to login. While some of the Instagram features are also available on the browser, Instagram focus is more inclined toward the mobile app, thus a browser can reach a limit regarding usual functions, which includes verifies.
First solution to the login loop:
In general, a login from the latest Instagram app version solves the loop issue. You just need to use a rooted android phone or emulator (pre-rooted Bluestacks) and install the latest IG app from the Google Play Store (or download an .apk installation file from Apkmirror). After you login inside the mobile app, the PV procedure can then most of the time be completed without further redirects/loops. But the glitch might not stop here, so read below for a secondary solution..