It would be catastrophic if the leaders also go wrong. In that case, they themselves would be in need of an infallible leader and so on.
On the other hand, God wants to leave no room for people to have excuses for their wrongdoing and it necessitates sending infallible leaders.
How can God give the responsibility of leadership to someone who may himself do wrong, make mistakes and commit sins?
Moreover, would it not be an insult to humanity if people’s leadership was to be given to a sinner?
The Quran cites Prophet Abraham’s (AS) prayer: “He (God) said, ‘I am appointing you as the leader of mankind.’ Abraham asked, ‘Will this leadership also continue through my descendants?’ The Lord replied, ‘The unjust do not have the right to exercise My authority.’” (Verse 124 of Surah Al-Baqarah)
The Quran also commands us to obey the Holy Prophet (PBUH) unconditionally and this command is proof of the prophets’ infallibility because if there was a possibility that they may make mistakes, God would make it conditional to obey them just like obeying parents, for all their significance, is conditional and God clearly says do not follow parents who have gone astray.
“But if they (parents) strive with you to make you associate with Me that of which you have no knowledge, do not obey them. And accompany them in this life with kindness; and follow the Path of he who turned to Me. To Me you shall return and I will inform you of all that you have done.” (Verse 15 of Surah Luqman)
A comparison of how the Quran commands us to obey the prophets unconditionally but obey parents conditionally will reveal that prophets are infallible and following them without any conditions is alright. As the Quran says: “He (the Prophet) does not speak out of his own desires. It is a revelations which has been revealed to him.” (Verses 3-4 of Surah An-Najm)