School anxiety depends on multiple factors that occur directly or indirectly in the teaching–learning process, such as going to the blackboard in class or reporting low grades at home. Other factors that influence school climate are social skills and coping strategies. That said, the aim of this research was to analyze the sources of school anxiety, coping strategies, and social skills in Italian secondary school students through an artificial neural network. For this purpose, a quantitative and ex post facto design was used in which the Inventory of School Anxiety (IAES), the Coping Scale for Children (EAN), and the Questionnaire for the Evaluation of Social Skills student version (EHS-A) were administered. The results showed that cognitive avoidance and behavioral avoidance coping strategies, together with the lack of social skills in students, are the variables that contributed the most to school anxiety scores in the artificial neural network. The conclusions revolve around the need to develop primary prevention programs.