Why did not Christ say that St. Peter was the greater, taking advanage of this occasion?

You must remember the sense of the discussion. Peter was not necessarily the greater from an aspect of grace and holiness. Eternal rewards depend rather upon Christian virtue than upon earthly office. St. Peter was chief in earthly office, although we know that St. John was called the beloved disciple.

Radio Replies Volume 1 by Rev. Dr. Leslie Rumble MSC and Rev. Charles Mortimer Carty