iPhone mirroring not working on MacBook Air after entering password

Are you following the steps here?

iPhone Mirroring: Use your iPhone from your Mac - Apple Support

Specifically:

If iPhone Mirroring doesn’t find your iPhone, doesn’t connect to it, or the connection is interrupted or times out, follow any instruction shown in the iPhone Mirroring window. If necessary, try these additional steps.

• Make sure that your devices meet the iPhone Mirroring system requirements.
• Install the latest software updates for Mac and software updates for iPhone. 
• Restart your Mac and iPhone.
• If either device is using Bluetooth or Wi-Fi intensively for another purpose, such as to stream audio or video to another device, discontinue that use and try again. It might also help to check for wireless interference.
• Check for VPN and other third-party security software on both devices. Similarly, the firewall settings on your Mac should not be set to block all incoming connections.
• Revoke access to your iPhone in iPhone Mirroring settings, then set up iPhone Mirroring again.
• If no other solutions work, sign out of your Apple Account on each device, restart, then sign back in.