1. Must the two be mutually exclusive? Teaching students irrelevant or outdated skills is a great way to encourage them to dismiss the profession as old, stodgy, useless, etc.

2. That's true. Is there a reason not to fudge the details of a current, employable technology stack?

3. Let's examine the logical extremes. On the one hand you have an incompetent teacher who can nevertheless communicate well. On the other hand you have a competent teacher who is a poor communicator. Frankly, I would rather have the latter. Otherwise, what's the point?