This can be for a number of reasons. Usually its just a setting that needs to be changed.
Before you begin, make sure you know the name of service the customer was trying to book.
Then check to see:
Is the Pack or Subscription applicable to this service?
Click Customers > Customer List > search for the customer and click them. From their customer profile, click the link to their Pack or Subscription.
Then click Appointment Services. Is the service listed here? If not, assign it.
Note that if the service is listed below, its included. The checkboxes are just used for removing services. Before moving on, are there any other services that should be listed?
Was the service set up to 'disable booking with memberships'?
To check if this is the case, click Appointments > Services > click the service.
Below, you'll find a section called 'who can book'. It previews the settings chosen for this service when it was first set up.
If the setting called 'Disable booking with memberships' is on, you'll see a red icon like the one below. To turn it off, click Actions (top right) > Edit > scroll to 'who can book' > toggle it off and save.