Helicopter instructor pilot reported an NMAC with a light plane in the pattern at 1B9 non-towered airport.

Narrative

I was conducting flight training with my student at Mansfield airport (1B9). We were using RWY 32 for left traffic patterns. At the time of the event there were 2 other aircraft in the pattern; with one on the downwind leg and another on base. The situation arose when the aircraft holding short of the runway decided to enter the active runway for a northbound departure whilst one aircraft was almost on final and we were on climb out on RWY 32.We were literally just at the departure end of RWY 32 at 575' when my student spotted Aircraft Y abeam us on his side (right hand side) making a turn to the right away from us. The aircraft had just made the departure call and next thing we know they were abeam us. Looking back at ADSB exchange this aircraft was at 400'; so less than 200' from us and only about 50-100 feet away from us horizontally. Both my student and I were taken aback by this departing aircraft for such reckless behavior and strongly felt the need to report this incident.Mansfield airport is a Class G airport; however; this should not allow pilots to make such close calls; especially with traffic in the pattern. This aircraft literally squeezed itself in between the landing and departing traffic instead of holding short to maintain adequate separation. They could have easily caused a mid-air collision due to their impatience and inadequate radio calls.We see more and more of instances of pilots at Class G airports not making radio calls to share their intentions and making good judgments calls for traffic separation.