There are security settings on the backend of the forums to help secure each and every one of your accounts from anyone that might try to login (there is no problem with that - it's a fail safe setup).
Basically, It is a double authentication that's always been in place. If you login from a private window then there is nothing that tells the forums that you are actually you, so you will get that authentication email to verify that it is you and not someone else.
This is why there is no issue when using a regular browsing window because you are logging in from a recognized device that has been used for your account on previous login. This is also the reason why you must authenticate every time when using a private window, each time it is different, that is the whole point of using a private window.
Also this could apply if you are using any kind of VPN.
It may even apply if you are moving around and the IP address changes.
Hope that clears things up a bit and sorry if there are any inconveniences, it is in place for the protection of all of our accounts on these forums.