Doesn't CFI have to have and instrument rating to teach instrument
flight?


Oddly, no. IMO, the FAA weaseled it way out of that one by redefining
what is taught to a private pilot as "flight by reference to
instruments", rather than "instrument training".

In reality, a distinction without a difference. A more honest
approach would have been to grant an exemption to CFI's for training
private pilot.