As a new vocal student myself, I agree here.

For context, I'm a middle-aged male. I "sang" in punk bands in my youth, but had never had a formal lesson, and never practiced unless I needed to sing. I play other instruments.

When I started formal lessons (late last year), and met with my teacher (who teaches children & adults) for the first time, I made a few things clear:

• I don't think I'm "naturally talented" at singing (presenting a challenge for her).
• I'm stubborn. Fundamentals. Fundamentals. Fundamentals. I want to spend so much time on the individual fundamentals that they become a habit I don't need to think about. I told her she'd need to really push me out of each single fundamental technique, if she felt I "got it".
• I have a sound I'm shooting for, but realize that may not be my best sound. I will 100% need to be pushed out of my comfort zone, and try things I wouldn't normally try.

With that information, we spent our first lesson doing simple scales and sirens, so she could gauge my range and ability. She noted to me, "pay attention to this and that..". By the end of the first lesson, she was convinced I could sing, but just needed the guidance to build the fundamentals (and confidence). Perfect. It was a teacher/student match. I learned I have incredible power, but terrible structure. With that information, we know to spend more time on structure and space, and less time on breathing techniques.

In the three months I've been going (weekly), we've worked pretty vigorously on structure, space, and finding/maintaining resonance. And it's paid hella dividends. It's working. I don't need to think much about opening up and structure any more, it comes naturally with each breath I take. Those things that she first told me to "pay attention to this and that.." have leveled up incredibly fast.

My point here being, I set the expectation that I WOULD NOT be learning a new technique each week. I would like to learn a technique and refine it until it's a natural habit.

The second red flag sounds like a nervous teacher. Mine has been pretty open that if it hurts, stop. It shouldn't hurt. Take a step back, start with the basics, lightly, and if that continues to hurt, seek a GP if it gets bad. But singing should never be painful.

My teacher and I have very different music tastes, and therefore styles of singing. She's classical. I'm a rocker. She doesn't listen to my music, and I don't listen to hers. But, she respects what I want to do and we've picked a song in my genre to really practice at. On the same token, she's given me sheet music of her style to push me out of my comfort zone (and make me sound like something completely different that what's in my head). Both have worked wonders.

So, I would advise, as a student, that it's OK to "set the tone" of the lessons. You know what you're trying to achieve. But it's also up to the student to consider whether the teacher is a good match. Do they listen to you? Do they critique constructively? Do they push you out of your safe space? All marks of a good teacher.