Of course I understand the principles of an adversarial system of trials. My question was how did this lead to prosecutors believing their job is to seek convictions rather than justice.

Well, if the adversarial system is effective, then it's the combination of prosecutors driving for convictions and defense attorneys driving for acquittals that produces justice. Hypothetically, only the judge is concerned with justice. And even then, only obliquely, because they only oversee justice of the trial process, not justice in general.

There are fundamentalists in law, just like in religion. A conviction exonerates the lawyer from any responsibility for injustice. After all, the opponent was declared or admitted guilt. Just as a religious leader exonerates himself from responsibility for enabling pogrom or ethnic cleansing as being the written will of the almighty.

It happened when their primary career performance metric became convictions.