Paul writes to Timothy about Alexander, whose faith had suffered shipwreck, and later he warns Timothy to be wise in dealing with him. (I Timothy 1:20; II Timothy 4:14) Initially, Alexander was a disciple of the Lord, but went astray; later, he lost his faith.
Coppersmith: Alexander was a metalworker. His profession could have included making idols. Was Alexander advised to refrain from making idols? Perhaps that angered him, and he left the faith?
Resisted our words: Paul writes that Alexander resisted his words. It could be at the court, Alexander was a witness who misinterpreted the words of Paul. In the city of Ephesus, the preaching of Paul made a great impact. The sales of miniature shrines and idols of Artemis were affected. Hence, Demetrius, the leader of the guild of metal workers, instigated a riot. Alexander made a defense on behalf of the Jews, that they were not associated with Paul or his Way. Yet, the mob rejected Alexander, also.
Informers: In the Roman Empire, some informers spied on fellow citizens and filed reports, many of which were false accusations. Alexander could be one such informer. He could have reported that Christians do not worship Caesar, and they eat and drink of the Body of Christ.
Warning: Since Alexander opposed and did harm to Paul, his hatred, envy, and anger may spill over to Timothy. The same bitterness with which Alexander opposed Paul, he will oppose Timothy also. So, Timothy should be prepared.
Divine Justice: Paul did not seek revenge. Instead, he committed to God for His righteous Justice at the appropriate time.
People who harm: As Paul and Timothy faced much harm, today, also disciples of the Lord face much harm. First, it could be ego and envy. Second, the truth is affecting their lives, families, influence, and livelihoods. Third, some people get a thrill or joy from harming others. Four, Satan could use them as instruments of unrighteousness. Five, Christians would be hated without any reason. (John 15:25)
Am I wise as a serpent and innocent as a dove? (Matthew 10:16)