Just to add (borrowing CXT's points- amended ofcourse)

Also as an Instructor:

Do you portray yourself as a worthy Sensei of said respect to start with?
Are you humble and peaceful or do you come across as arrogant and cocky etc.? Consider it as are you a Miyagi Sensei or a CobraKai Sensei?

How do YOU view your students training?

If its "just business" to YOU then why would you care what the dude/dudette that trains with you thinks about you?

Its a 2 way thing, an instructor can feel betrayed as if he/she has dedicated their time to your training then you move on and look elsewhere it can be a big hit to the "ego" of the Instructor (although for me as long as it doesn't affect the individual's skill level I'm actually honoured)
A man is but the product of his thoughts what he thinks, he becomes.