I find the gentle poses okay. The last actual class I went to I wouldn't do a head stand. I told the teacher I didn't think my neck vertebrae were designed to support my body weight and I wouldn't do it. She tried to talk me into it like I was a coward, and said she would catch me if I fell. I said I thought I was being pretty logical and didn't see the point of risking injury. There are inverted poses that don't involve balancing on one's neck. Then some of the other people in the class thought I had a point and wouldn't do head stands either after that and things kind of went downhill from there.
That's the problem with some yoga teachers. There are many alternatives for inversions, for example, lay on your back, put a block under hips and lift your legs up. If you do this at the wall (and in that case I'd use a bolster), then it's restorative and great inversion.
With a proper headstand you shouldn't have any weight on your neck. All of the support should come from your base, consisting of your forearms and shoulders. This requires a bit of upper body strength, which a lot of us are lacking. This is why headstands are dangerous, because then we compensate by putting weight on our neck instead of using our upper body.
I can understand why teachers like headstands. A lot of people have a feeling that they can't do it because they are scared of being upside down, so it's nice to break this line of thinking. It also has that yoga coolness factor. But there's never a good reason to suggest it if the person isn't ready. An excellent alternative is to use to folding chairs against the wall with enough space between the chairs for your head. Make sure you have cushions on the chairs and they are on a no slip surface. You can then rest your shoulders on each chair with your head in between and lift up against the wall. This is better with an assist if you've never done it before (or even if you have). It's a great way to do a headstand with zero pressure on the neck. I enjoy doing this one at home sometimes because it's restorative.
I'm glad you pushed back. Too many people don't, which can be a problem with classes, especially if you are new to yoga. I enjoy the classes because I always learn something or can try something new, such as the chair headstand. If I didn't attend classes, then I think I'd get bored (not to mention procrastinate). Part of what makes yoga fun for me is that it's not repetitive, so even after four years of practice I'm still engaged. Fortunately, I live in an area with a lot of good yoga teachers, so it's not difficult to find a challenging class where I'm free to make modifications.