Wow. It sounds as if this counselor is doing some serious gatekeeping. If you're satisfied that he's not going to shut you down in the future or make demands on your transition, or if there's NO other counselors available, stick with him.
Otherwise, shop for a new one. If you're in the US Psychology Today has a fairly compensative list of available counselors by region, who deal with transgender issues. That's where I found mine, and he's pretty open.
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