My Apple Watch doesn't unlock my Mac

I had this issue also. I finally resolved it. Here's how:

1. Go to System Preferences
2. Click Apple ID
3. Click Overview
4. Sign out
5. Restart your Mac
6. Open System Preferences
7. Click Apple ID, and
8. Sign back in to your iCloud account
9. Go to System Preferences/Security & Privacy/General and check "Use your Apple Watch…"

Worked for me. Hopefully it will for you, too.

See the 'How to set up Auto Unlock' and 'Learn more' sections in:

Unlock your Mac with your Apple Watch - Apple Support