@jandal ...you have reached out here. IMHO, your T pushing you to do something you're not comfortable with, and may also isolate you from existing friendships (not everyone is comfy with, or knows how to respond to one with PTSD).
The fact that she keeps bringing this issue up, and taking valuable time away from discussing your other concerns, to me, doesn't sound right. As others have suggested here, there's ways for you to build your support system when you feel ready to, and in ways that may not alienate them from you. If it were me, I'd tell my T that I have a plan in place for building a support system..as others here have mentioned...and that she needn't worry or bring it up again, until such time as YOU feel it necessary.
I get how some T's want to bring us out of our comfort zone in order to move forward. Yet, when it comes to revealing trauma to others, that takes time and much vetting out who and what we share, in order to feel our secrets are safe with them. In some instances, that could end up biting you in the butt. Takes a lot of discernment who to open up with. That's why we seek help with a therapist, cuz they have a confidentiality agreement to stick by. Non-T's don't.
If your T feels she needs you to have more support in order for her to feel less burdened or whatever, then perhaps she's in the wrong biz.
I've opened up to what I deemed were friends at the time, only to have it get passed around as my being mentally unstable & a 'stay clear of her' attitude by the time it got to the end of the 'Chinese Telephone' line.
Sometimes we don't make good choices when clouded by PTSD, and have to do more work with a T to get to a point where our vetting skills are clearer.
I hope all goes well with your therapist, and you two can come to an understanding...even if it's a agree to disagree moment. Best.