Why would clients not see options to schedule if I have available time in my calendar?

There are three factors:

1. Appointment type permissions: make sure the clients have the necessary permissions to access and schedule with a certain appointment type.
2. Available time duration in relation to the appointment type duration: make sure the available time intervals are long enough to allow at least one scheduling option. For example, if you have an appointment type of 60 minutes in duration and the available time you schedule is 50 minutes, that is not enough time for one appointment of that type. Also, keep in mind that times blocked (breaks) before and after in the appointment type settings are also included (they count).
3. In the Calendar Settings there is a setting for allowing clients to schedule with a minimum time in advance. If you allow the scheduling with a minimum of one week in advance and you only have available time over the next five day, then the clients will have no option to schedule. So, keep this setting in mind as well.