GA pilot reported a gust of wind caused the aircraft to ground loop on the runway during landing.

Narrative

On Day 0; I was flying Aircraft X under 14 CFR Part 61 Sec 61.57 Recent flight experience: Pilot in command (a) General experience at ZZZ Airport. There was a 3 to 5 knot crosswind from 180 degrees to Runway XX. During one of the landings; I experienced a ground loop. After that; I landed on the grass south of Runway XX. The landing was uneventful. However; I did notice that rudder control was insufficient at idle RPM; as the aircraft started to weathervane into a wind gust that was greater than 5 knots; according to the windsock which has no long limp. I had full rudder control to the left as the aircraft continued to start turning to the south. I added a couple hundred rpm; and the rudder control came back. The landing was successful. The aircraft has nonstandard larger tires that cause problems when landing on concrete.I have over 450 logged hours in a conventional aircraft (taildragger). I was getting current in the aircraft to give flight instructions to the owner who recently purchased the aircraft to obtain his Sport License. The ground loop caused damage to the aircraft. There was an observed tear on the right wing of about two inches of scraping aft of the wing tip. There was a ground strike on the right horizontal stabilizer. Both areas need to be inspected and repaired by a Certified Mechanic under 14 CFR Part 43.My experience with this aircraft has convinced me that primary instruction landing practice on concrete will not work for a new student. This aircraft needs to be flown off grass strips.