being equal

I think they meant it more in terms of you being able to make your own decisions, and to have your decisions respected.

Not a situation where the T says "You have to do this," or "I'm the one in charge here," or anything like that. That your opinion and VOICE is equally valid in the relationship.

You should be equal partners in the relationship of YOU GETTING BETTER. That doesn't mean that you get to decide to talk about your T. It's not about your T. It's about you.

My $.02

My T and I Have a genuine respect for each other. For me that translates into feeling his equal.

In terms of equality - one knows going in what the terms of the agreement are and has consented to them and if one does not like the basic terms, one finds someone else - ie. I give you x dollars for x amount of time = so scenario one does not seem unequal to me.
The purpose of the relationship is to tell the therapist about yourself - not to find out about the therapist -as a lawyer, I do not share info about myself with clients and they do share info about themselves with me - it is relevant to me to fully defend them in a criminal defense situation to have info about them - not so much them about me. I do not know anything about my financial advisors personal finances but they know a lot about mine and so forth = for me this is not the sort of thing that creates inequality.
For me it is about the therapist (or doctor = I find it happens more often in health fields for reasons probably not relevant here) acting superior, not revealing information that I ask for about technique or therapy or such, and trying to set themselves up as an authority figure rather than simply someone with different knowledge than I have.

I understand this.
On the other hand, my T says she respects me (I have no reason to doubt her) and I also respect her; but for me that translates into realizing that she is worth ten of me any time.

So true! But I think that what they mean is to respect the patient as a human being just like him or her... It's like when you go to the gyno. They're treating you, but they are just like you - and you know it and feel that respect, you won't say: "You've seen my private parts, now I want to see yours too!". Cause we're the ones looking for help, looking for a "service"

I don't really think of my T and I as equals, because there is an inherent power differential in the relationship. How she respects and uses that differential is more important to me than being equals. Doesn't mean I still don't want to be equals in some ways, but I understand that in the grand scheme of things that's not really possible.