Yes, I know that in theory they are both wage slaves.

But, if there is a need to cut, are they in the same class?

I would argue that, what is currently bought with 3000€/month makes that said salary unsustainable from a planet-wide perspective (resources).

If everybody made 3000€/month and had the ability to acquire resources equivalent to it, we would need probably 5 or 6 planets.

You seem to be fixated in the word "teacher". I seem to be fixated in an income difference (and job security is also qualitatively different) of 6x.

It in fact happens in the teaching profession in Portugal: rules that feel very good for part of the class, are pretty bad for another part.

While that black and white view of oppressors and oppressed seems to make sense, it does not preclude a complementary view that things can be a bit more complex than that.