1) Instructor demonstrating the basic casting stroke
The instructor demonstrates how to make a nice tight loop cast (starting around 5:30). His casting stroke is smooth, compact (no 'large movements') & elegant. Look at his casting style: (almost) vertical casting stroke (aka San Fransisco's Golden Gate casting club style) using his shoulder and (mainly) lower arm, all moving in one plane. Similar to how you move your arms when you run. This casting movement (a '2D' movement') is quite easy to get it, especially for beginners.
2) Inconsistency of instruction
Later on, while helping a student he holds the student's hand and shows the casting movement (around 8:55). The instructor's casting movement is the same vertical casting style while the student is 'forced' into the side arm (like when you raise your arms after 'hands up!') casting stroke with his lower and upper arm to the side in a 90 degree position making casting movement very awkward. This position also puts lots of stress on the shoulder.
This side arm (using predominately your elbow) casting movement is a much more complex '3D' movement as it involves your elbow, upper arm and a bit of your shoulder joints (3 joints!) all moving in different directions. This is quite confusing for beginner. Try casting using this movement with your non casting arm and you know what I mean š.
I know it's not easy to stand next to each other and positioning both arms symmetrically. However if you want to teach the student the casting stroke you promote, the movement of the instructor needs to position the student in the casting 'path' you want to instruct, otherwise you're confusing the student (and the student is probably not even aware that he is confused!). This inconsistency will result in the student learning the 'wrong' casting stroke. See the student's casting style that he is trying to master around 8:40, look at the student in the pink sweater next to him too, same casting movement.
Ps.
Casting styles is a whole different subject on its own. Different casting styles can be used depending on the type of fishing (for instance with weighted flies), conditions (wind) and/or target (under a branch). One style isn't better than the other, just be aware that when teaching students one needs to be consistent and not mix casting styles in the instruction.
Here's an article about different casting styles.