Owning a program, scheduling it, and actually training are three separate things. This trips people up, so here is the short version.
Owning a program
When a coach assigns you a program, or you buy one, it lands in your library under Training. Nothing is booked in and nothing is logged yet — it is simply yours.
Training now
The Start (or Continue) button on the program page opens the next session and starts logging. This is the only button you need in order to train. You do not have to schedule a session before you can do it.
Scheduling
Add to Calendar lays the program's sessions onto dates. It is a planning tool: it helps you see which day you intend to train, and it puts the sessions on your calendar view. Scheduling a session does not log it, and skipping the calendar entirely does not hold your program back.
Use the calendar if you like planning your week in advance. Otherwise just hit Start when you are in the gym.