Conduct Disorder (CD): This diagnosis is the most likely due to the presence of aggressive behavior towards people and animals (shoving classmates, attempting to set fire to a trash can), and destructive behavior (attempting to set fire). These behaviors are key criteria for Conduct Disorder.

Oppositional Defiant Disorder (ODD): Characterized by a pattern of angry/irritable mood or argumentative/defiant behavior, which is evident in the child calling students names and shoving classmates. While the severity of attempting to set a fire might lean more towards CD, ODD is a consideration, especially if the behaviors are less severe and frequent than required for CD.
Attention Deficit Hyperactivity Disorder (ADHD): Children with ADHD can exhibit impulsivity and aggression, which might manifest as shoving or calling names. However, the deliberate attempt to set a fire might not be fully explained by ADHD alone, suggesting the need for a comorbid condition.
Disruptive Mood Dysregulation Disorder (DMDD): This condition involves severe temper outbursts and persistently irritable mood. The aggressive behavior and name-calling could be part of the irritability seen in DMDD, but like ADHD, the severity of attempting to set a fire might suggest a need for an additional diagnosis.

Bipolar Disorder: Although less common in children, bipolar disorder can present with severe irritability and aggressive behavior. The attempt to set a fire could be seen as a severe impulsive act, which is sometimes observed in manic episodes. Missing this diagnosis could lead to inappropriate treatment and worsening of symptoms.
Trauma- and Stressor-Related Disorders (e.g., Post-Traumatic Stress Disorder - PTSD): Children who have experienced trauma may exhibit aggressive behavior as part of their symptomatology. It's crucial to assess for any history of trauma, as the treatment approach would significantly differ from other diagnoses.
Neurodevelopmental Disorders (e.g., Autism Spectrum Disorder - ASD): Children with ASD can exhibit aggressive behaviors due to frustration with their environment or as part of their disorder. It's essential to consider ASD, especially if there are other signs of developmental delays or difficulties with social interactions.

Intermittent Explosive Disorder: Characterized by recurrent behavioral outbursts representing a failure to control aggressive impulses. While this could explain some of the behaviors, the presence of other symptoms like attempting to set fires and consistent aggressive behavior towards others might suggest a more pervasive disorder like CD.
Psychotic Disorders: In rare cases, children can exhibit aggressive behavior due to psychotic symptoms. This would be a consideration if there were other signs of psychosis, such as hallucinations or delusions, which are not mentioned in the scenario provided.