Continuing on with what JamesNoBrakes was getting at: as an instructor, and pilot in general, you need to understand what the privileges and limitations are of your pilot certificate. FAR 61.193 lays out the privileges, "A person who holds a flight instructor certificate is authorized within the limitations of that person's flight instructor certificate and ratings..."

So, what are the privileges of the Instrument Instructor? They are to provide instruction for the Instrument Rating which is a privilege that is added to a previously existing pilot certificate. Definitions are extremely important here, and FAR Part 1.1 under Definitions and Abbreviations defines a rating as something which "sets forth special conditions, privileges, or limitations."

Although the instrument training received during the private pilot course is eventually counted towards the instrument rating, it cannot be taught by a CFII because that instructor is limited to instruction relating to the added rating, and not to the initial certificate.