Why is the iMessage screen sharing option not available? What causes it to be greyed out?
(see screenshot, green arrow)
Assuming that your contact is an iMessage user, a grayed screen sharing button indicates that he can't receive screen sharing at this time.
He may have disabled screen shaping in the Mac settings for instance, or he may be using his iPhone so he cannot perform screen sharing.
Ask your friend if he is using his Mac and ask him to enable Screen Sharing in System Preferences → Sharing.
Make sure the person is signed into iCloud (check System Preferences>iCloud). This fixed it for me.