The author here seems to be using "paraphrase" to mean mean both "mirroring" (repeat back using speaker's words) and "paraphrasing" (repeat back using listener's words). I think there are contexts when each is appropriate.

For example, if I (speaker) am giving you (listener) instructions, it's good for you to paraphrase. That shows me how you are interpreting my language and that allows me to clarify. Mirroring doesn't allow for this because no new information is provided:

- Speaker: Could you sort all the files and destroy duplicates?

- Listener: You want me to put the files in alphabetical order and throw them out.

- Speaker: Yes, but by destroy I meant shred.

But there are cases where it's more important for the speaker to be understood. Perhaps they are feeling hard emotions and need to be heard, or (and I think this is the real use case for mirroring) when the speaker is still working through their feelings or thoughts on a subject. They are using speech, in a sense, to think.

- Speaker: I think it's bizarre that the PM wants to push this along so quickly.

- Listener: You think it's bizarre that the PM wants to push this along so quickly?

- Speaker: Well... not bizarre. It's just surprising because there is no external deadline for this work.

Here mirroring gives the speaker an opportunity to see how their words sound coming back to them and it gives them an opportunity to clarify and add.