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I've seen a lot of therapists in my life. The first one was in 8th grade and was a red flag, the second one was in 10th grade and she was only pediatric but retired anyway and I do miss her, the third one was also in 10th or 11th and she sucked and our insurance stopped covering the place, then another in 10th or 11th that was pretty good but through the school-based health center so I couldn't see her upon graduating high school, the fifth was in the college counselling center but was pretty meh. I only saw her because I wasn't able to go anywhere else. The sixth was a walking red flag. Then I met my seventh therapist, who I see currently! This is not counting clinicians in group therapy, IOP/DBT programs, or med providers. I've only had two med providers, one through the college counselling program and then the one that I have now, who is amazing (although she always runs late for meetings which I've been told is a little unethical. I deal tho.).
I think I connected with the ones I did based on the way they built rapport with me. Of course they wanted to know why I wanted to be in therapy and what I wanted to get out of it but they didn't make me dump my deepest, darkest secrets in the first session or anything like that. Their personalities seemed to click with mine as well. They told me like it is but weren't rude about it, and we were able to talk about good things sometimes too instead of just the bad things. They encouraged my safety and dealt with my willfulness pretty well.
I did notice some red flags with two of my old therapists. One I only saw for like two sessions and my mom yote her because she was useless, but the other one I had as an adult. Her response to my self harm was basically "don't do that," which...useful isn't it? She would go over with other patients and therefore run late getting to my session. I took Medicaid transport to see her, so I was on a strict time schedule and sometimes would only have half an hour sessions instead of a full hour because of it. She also answered texts from other patients in the middle of my session, which I get that they could be having issues too but it's my session now, please pay attention to me. She also ate cereal at least once when we went virtual. So, maybe go for someone who doesn't do those types of things.