It sounds odd to me. I've used two online therapists in the past to get referrals. I've had my buttons pushed, but not in the same way.
The first I wrote a short message to, basically saying who I was/what I wanted/asking about her availability. She was slow to get back to me, but we scheduled a session. At the start of our session I reiterated what the purpose of therapy was for me (to get a referral), and answered whatever questions she asked. I don't want to say that she was bad at her job, it could be that I just really don't like to talk about myself. It really felt like pulling teeth working with her. Every little thing I said was nitpicked. After three sessions, she refused to even estimate when I would have a referral, so I fired her.
Next one was much better. He had a 5+ page biographical form that you filled out and sent back. First session was mostly clarifying questions based on the form, and what I wanted. We met 3 times and he wrote my referral. Very knowledgeable, affirming dude. Never once made me feel like I was being ignored or that I wasn't getting through to him.
Are you planning to work with this therapist online? Could it be that they just aren't used to email correspondence to get to know a patient (maybe their practice is predominantly in person sessions)?