@Suchu0 Click on your profile picture and and go to Settings. In the right handside is a Contact Information. Hit edit. Put the email you want to use there and save it. Then follow the steps below. If it doesn't work the you will have to call AirBnB Australia +61 2 8520 3333.
Here are the full steps.. You need to sign in with Facebook or Google to proceed' dialog:
1) Click on your Profile Picture -> Settings -> Privacy -> Social Connections -> untick Share my activity
2) Edit profile -> Trust & Verification -> disconnect Facebook or Google
3) Log out
4) Try to Log back in with only your email. If you get the 'You need to sign into Facebook or Google dialog' continue with step (5)
5) Log out if you're logged in. On the login page, click FORGOT PASSWORD. This will send a reset password email - go through that and reset your password. Then login again with your email. No more mandatory Facebook or Google dialog!