There are so many forms of Yoga that are not based upon asana practice. Jnana, Bhakti, Karma, Kundalini, Mantra, and Yantra could be added to the top of the list, but there are many more. Patanjali mentions Eight Limbs of Raja Yoga, but asana is only one of them, and it is not the first limb mentioned. For good reason, Niyama and Yama are the first two limbs.
Lately, I have received a number of similar inquiries from Yoga teachers about this subject. Yoga is the application of concepts we learn, within each session, applied to daily living. To hear about teachers who fail to understand that Yoga is more than a physical exercise is ironic. Perhaps these same Yoga teachers never read the Yoga Sutras or heard of Patanjali. Possibly, physical prowess has inflated the ego so much that reality is fading away from the mind.
It is always very disappointing to know, meet, or hear about teachers who make judgements, inflate their egos, degrade their students, and completely miss the concept that Yoga is a complete lifestyle - not a physical exercise.
If Yoga were all about flexibility, we could make our children and grandchildren Swamis right now. A female Olympic gymnast is in her prime at 15 years of age. She can do all the fancy asanas, without attending a Yoga class. Is this Yoga? When she retires from gymnastics at 17, should we call her Swamini?
One more point to make: Yoga is often considered to be a science or art of living. The therapeutic application of Hatha Yoga is to reduce or end suffering from ailments. A competent Yoga teacher understands that each student's body is different. Standing on one hand, to inflate our importance, will not help our students benefit from the therapeutic application of Hatha Yoga.