C172 pilot reported an NMAC after an aircraft turned the wrong way during a go-around and verbalized a lengthy radio call; preventing ATC from warning of traffic conflict.

Narrative

While in reporting aircraft [and] was downwind for right traffic [for] RWY XX approaching XY numbers; [I saw] an aircraft (C172) that was cleared to land decided to perform a go-around. In an attempt to avoid the upwind traffic (C152-slower); the go around aircraft made an immediate right crosswind turn. The right crosswind turn placed the go around aircraft and reporting aircraft on a collision course. While this was happening; ATC queried the go-around aircraft reasons for go-around and potential need for assistance. The CFI onboard the go around aircraft responded lengthily (I was doing soft field landing and had to go around etc...) while making the right crosswind turn. The reporting aircraft's instructor took over the controls from the student and performed a wide left 360 degree turn to avoid the go around aircraft. The go around aircraft's decision to over communicate prevented ATC from announcing a potential conflict. This incident highlights the importance of see and avoid and exercising situational awareness in the traffic pattern.