Just a easy question

If you know your Microsoft account information but still can't sign in to your account, first confirm that there are currently no Xbox Live service alerts. If there are no current service alerts, browse
a list of possible errors for information about common sign-in and Microsoft account error messages. If you don't see your error listed, use the Error & status code search tool to look up the error code and find information about that specific error. If neither
of those work, go to your Microsoft account online.
Learn more

What you could do is put his gamertag on your system, set your system as his "home" system. Then have him download your gamertag and set his system as your "home" system. This allows both of you to purchase any game and share between the two of you and play
together but only works between you two. Now if you remove his gamertag afterwards and you didnt purchase the game, you lose the game since the game owner is linked to account not system.

Be aware that sharing account information does violate the code of conduct. So you would not want to give him your login information if you were to do this.

What you could do is put his gamertag on your system, set your system as his "home" system. Then have him download your gamertag and set his system as your "home" system. This allows both of you to purchase any game and share between the two of you and play
together but only works between you two. Now if you remove his gamertag afterwards and you didnt purchase the game, you lose the game since the game owner is linked to account not system.

Have you tried removing and re adding your profile to your console?

Are you talking about Live? You can always check the status of Xbox services at

https://support.xbox.com/xbox-live-status

Hope this helps!