This is a horrible thing to say. Of course a therapist's feelings come into it: their humanity is what makes them so much better than getting textbook feedback from an AI. Their humanity's the reason we don't feel some practitioners are right for us and others are.
Yours isn't the only reply asserting the view that therapists aren't allowed to bring their own feelings (and personalities, by extension) into the room. That idea's unrealistic and cruel.
We expect all sorts of professionals to bring their feelings - modulated if appropriate, but still present. We also expect them to absent themselves if their personal feelings make the relationship/consultation/service sub-optimal. If you were seeing someone about a hysterectomy, for instance, you'd likely welcome some concern but would want a different HCP pretty quick if they expressed a belief in woman's destiny as child-bearer, regardless of any issues.
A good therapeutic relationship is a "relationship", comparable to romantic partnerships in some ways but different in that it's understood to be time-limited and that there's a different power dynamic. Good therapists use a lot of skill to manage this dynamic for the client's benefit, the end goal being to arrive at a point where the client can manage her own feelings, boundaries and expectations.
Bad therapists use it to keep their clients dependent on them. Some even become co-dependent with their clients. Weirdly, some respondents here seem to be wanting this sort of enmeshment - I don't know if any of them are in therapy, but I hope not. OP's practitioner didn't do anything wrong. She didn't ghost her, insult her or dump her by text! She explained that she felt OP was enmeshed and, correctly, that the relationship would therefore be unhelpful if continued. Perhaps she also felt she, herself, was at risk of over-involvement: we can't know that but, if she did, it multiplies the reason for ending it.
She sounds like a mature, thoughtful practitioner. It's very disappointing for OP - and I hope your later discussion about her continued engagement as part of your maternity team, @AreYouThereGodItsMeHarriet, has both reassured you and allowed you to set new goals regarding your own emotional boundaries and relational expectations 