GA pilot reported an NMAC while entering the traffic pattern at a non-towered airport. While on crosswind; the reporter was overtaken by an airplane that passed them on the left within a few hundred feet; instead of passing on the right as required by the FARs.

Narrative

Approaching ZZZ from the northwest; listened to the CTAF for traffic twenty minutes out. Traffic was light until I got to a few miles from the airport. I initially was planning to cross midfield to enter downwind for Runway XX as the wind was out of the south at ten to fifteen knots on the surface. But an aircraft called in from the southeast and was going to enter the downwind at a forty-five-degree angle. When I was about ready to cross midfield; the aircraft called entering downwind. I continued on the upwind leg and then announced I would enter crosswind for Runway XX. An aircraft having taken off about a minute earlier and I had that plane in sight climbing out on the departure leg. As I entered crosswind; another plane departed intending to stay in the pattern. I was at cruise speed of 85 knots but with a twenty to twenty-five knot headwind at a thousand; I was only doing a ground speed of 60 to 65 knots.A pilot called me and asked if I had him in sight. I believing it was the aircraft having departed earlier said I did. The other pilot in the cockpit with me had pointed at the plane and I said to the pilot with me to keep track of the plane.I began to rock my wings for several seconds to help the last plane to depart to see me on the crosswind leg I was still on. I was then asked to turn out to the right while on crosswind. I did as requested; continued to look for traffic.A few seconds later; I saw a Piper Arrow pass me on my left within a few hundred feet of me at the same altitude having come up from behind me. I was then given a lecture on the CTAF that entering on crosswind was a very dangerous thing to do by the pilot who was clearly a flight instructor with a student to make a point. I decided not to bother to get into a shouting match as flying the airplane; both mine and the other pilot's plane was more important.What was wrong with what happened? First; the plane who I had a conflict with saw me on crosswind and did not give way to me as I was clearly on the right. All he had to do was have his student do was to alter course a little to the right to pass me as required by FAR. Second; an over taking aircraft by FAR is to pass to the right and well clear of slower aircraft. Finally; by allowing his student to come so close to me was operating in a careless manner.Based upon the amount of flight training conducted by the large university flight school; they need to have a control tower; to avoid potential mid air collisions. Until then; even though I have stopped there many times; I will avoid this airport.