Not only is it that a parent “should not” be a confirmation sponsor, but canon law states that a parent cannot be a confirmation sponsor.
A person who would undertake the office of [confirmation] sponsor must fulfill the conditions mentioned in canon 874. It is desirable that the sponsor chosen be the one who undertook this role at baptism (canon 893 §1-2, Code of Canon Law).
Canon 874 is the canon that provides the qualifications for baptismal sponsor, indicating that the qualifications for confirmation sponsor are the same:
§1 To be admitted to undertake the office of sponsor, a person must:
1° be appointed by the candidate for baptism, or by the parents or whoever stands in their place, or failing these, by the parish priest or the minister; to be appointed the person must be suitable for this role and have the intention of fulfilling it;
2° be not less than sixteen years of age, unless a different age has been stipulated by the diocesan bishop, or unless the parish priest or the minister considers that there is a just reason for an exception to be made;
3° be a Catholic who has been confirmed and has received the Blessed Eucharist, and who lives a life of faith which befits the role to be undertaken;
4° not labor under a canonical penalty, whether imposed or declared;
5° not be either the father or the mother of the person to be baptized.
§2 A baptized person who belongs to a non-Catholic ecclesial community may be admitted only in company with a Catholic sponsor, and then simply as a witness to the baptism (canon 874, emphasis added).
Show the candidate and the candidate’s father these canons and tell them politely but firmly that another sponsor must be chosen.