I think countertransference usually refers to feelings stirred in the therapist in response to a client's transference. This can be useful in therapy but the therapist needs to be aware of what is happening and be skilled enough to deal with it therapeutically.
A therapist can also have feelings towards a client which originate in themselves. My therapist told me last year that he felt paternal feelings towards me and these feelings unconsciously contributed to a rupture we had. I called it countertransference and he said he didn't want to use that word because he wanted to be clear the feelings originated in him.
I think any feelings are fine to be honest, so long as the therapist is self-aware and recognises their own stuff. My T's paternal feelings were only problematic when he wasn't aware of the fact they were impacting on his actions; since he's become aware of them he's kept them in check and I imagine on some level I receive those paternal feelings and they contribute to the sense of safety I have in my relationship with him.
So self-awareness in the therapist is key I think.