Why is the schizophrenia medicine clozapine controversial?

Because of risk of severe potential adverse effects.

Major ones are Agranulocytosis (bone marrow toxicity) and Myocarditis (inflammation of the heart).

Clozapine is an antipsychotic medication used to treat schizophrenia that can cause potentially serious side effects. Clozapine, also known as Clozaril, is part of a new generation of antipsychotic medications known as second generation or atypical antipsychotics. This class of drugs emerged in the 1990s and has demonstrated great potential for reducing some of the uncomfortable side effects associated with the older, first-generation antipsychotic medications.

While clozapine is very effective at reducing hallucinations, delusions, and psychotic symptoms of schizophrenia, it can cause serious health issues. Clozapine can cause a condition called agranulocytosis, which can result in a drastically low white blood cell count. If left unchecked, infections in the body can occur, resulting in the risk for serious illness and possible death. People who take clozapine need to have their blood checked on a weekly or biweekly basis. This can be time-consuming and costly, making clozapine an undesirable option. However, people do choose to take clozapine when it is the most effective medicine at reducing symptoms of schizophrenia.