What were Hymenaeus and Alexander’s sin?

Answer:

"This charge I commit to you, son Timothy, according to the prophecies previously made concerning you, that by them you may wage the good warfare, having faith and a good conscience, which some having rejected, concerning the faith have suffered shipwreck, of whom are Hymenaeus and Alexander, whom I delivered to Satan that they may learn not to blaspheme" (I Timothy 1:18-20).

"And their message will spread like cancer. Hymenaeus and Philetus are of this sort, who have strayed concerning the truth, saying that the resurrection is already past; and they overthrow the faith of some" (II Timothy 2:17-18).

"Alexander the coppersmith did me much harm. May the Lord repay him according to his works. You also must beware of him, for he has greatly resisted our words" (II Timothy 4:14-15).

Assuming that there aren't multiple people named Hymenaeus and Alexander being talked about we can see a few hints in the above passages.

• They had rejected the faith. But this Paul is stating that they no longer believed or taught the doctrines taught by the apostles.
• The doctrine they were teaching was blasphemous. Blasphemy is defended as, "But the person who does anything defiantly, whether he is native or an alien, that one is blaspheming the LORD; and that person shall be cut off from among his people. Because he has despised the word of the LORD and has broken His commandment, that person shall be completely cut off; his guilt will be on him" (Numbers 15:30-31, NASB). Blasphemy is the defiant, willful, purposeful breaking of God's commands. Thus Paul is stating that their false teaching isn't due to being deceived but a willful choice to defy what they once knew to be the truth.
• Hymenaeus was teaching that the resurrection, and by implication the second coming, had already occurred. Most assume this means that he was teaching there was no resurrection from the dead (I Corinthians 15:12), but only a moral resurrection at conversion (as taught in Romans 6:4). Such false teaching would remove any hope in a future life after death.
• Thus another charge against Hymenaeus is that he was causing other people to lose their faith by his false teachings.
• Alexander is only said to be strongly resisting the teachings of the apostles.