I accidentally logged out, and now I can't log in. I made new account and it logged in. Then I tried to login with my main account, but it just keeps trying but won't go to the loading screen and it won't log me in.
Try turning your phone off and reseting the wifi I know I've had to do that with mine a few times.
This was on an earlier version of the game, but could still work:
Somewhere in your settings you should see something like "Recently used devices". This depends on your device (for me it was in Sign-in & Security, under Device Access & Notifications). Remove the device you cannot log in with. Open Pokemon GO to get the google account permissions prompt again.
After I did this I was able to go back to using another account. I too had the never ending loading as you explained.
Try going into the settings on your device, turn on airplane mode, count to 30 then turn it back off and try the login again, this forces your device to connect with the best access point available for data transfer, hope this helps. If that doesn't do it, be sure you're not logged in on any other devices, and then if all else fails uninstall/reinstall. Still no luck Google your device and check how to update any OS level drivers, and double check that you dont have anything disabled relating to data transfer. If none of these work let me know I could probably think if a few other things to check.
Quick question, did you try logging in on a different device?