Verbal and non-verbal interactions that occur daily between teachers and headteachers, teachers and pupils, and among pupils can generate conflict that may adversely affect teaching, learning, and schooling effectiveness. Little attention is, however, paid to the quality of relationships that exists between teachers and pupils, among teachers, among pupils, between teachers and their school heads, and between schools and their local communities. This study sought to investigate conflict prevalence in Ghana’s primary schools, and how relationship conflict is understood to affect teaching and learning at the level of headteachers as administrators, teachers as classroom managers, and pupils as learners, and direct beneficiaries of primary education. Using data gathered via interview, questionnaire administration, and observation in 30 public primary schools in 10 circuits of one district of Ashanti Region, the findings revealed a high prevalence of fighting, heckling, bullying, and other forms of relationship conflict among pupils; strained teacher–pupil relations due to insolence, indiscipline, and use of offensive language; and teacher–parent arguments and quarrels due to harsh punishment and verbal assault of pupils. Teacher–pupil conflicts may extend to teachers excluding the affected pupils from teaching and learning activities, denying them the rights to ask and answer questions, and have their class exercises marked, leading to lowered pupil self-esteem, reduced concentration during lessons, and passive involvement in learning activities, which could result in truancy and school dropout. Strengthening guidance mechanisms and encouraging peer mediation could significantly curb conflict in school environments and thereby raise educational standards in the district.