One question I always ask my students after completing a beginner riding course is if they feel comfortable enough to ride on the street. I ask this for a couple of reasons; one is to help those who might be too confident after the training.
I often compare skiing to motorcycling. I like to do this because I am myself a beginner skier. I have had one lesson and a day on the hills. This helps me empathize with my students since we are at about the same experience level.
If I get a student who I believe is not quite ready to get into a traffic mix, I often use the Black Diamond analogy. Most of us would agree that after one or two ski lessons on the mountain that we would not be ready for the "expert" Black Diamond runs. Depending on the area you live, riding in traffic can be very difficult, pushing even an experienced rider to call upon all of their skills.
The first couple of months can be the most dangerous for a new rider. They are using a large portion of their brain power just to complete the tasks of getting the motorcycle going. Balancing clutch, throttle position, brake pressure, handlebar inputs etc. It's only until they can complete these tasks without "thinking" about them that the brain power can be focused on the other threats out on the road. I recommend plenty of "parking lot" practice of the techniques we teach in the school before adding too many other factors.
Just as you would master the Bunny Hill before you moved on. Master the parking lot before hitting the road. You will have more fun and be a safer rider.