The Prophet (PBUH) asks for Allah's forgiveness, but not due to committing the sin, and not even due to the thinking of the sin, rather, because he thinks that he has not worshipped Allah in a way Allah (J) deserves. [1]
Question:
If the Prophet is infallible, why in the noble Quran, he is ordered to ask forgiveness?
«فسَبِّحْ بِحَمْدِ رَبِّكَ وَاسْتَغْفِرْهُ إِنَّهُ كَانَ تَوَّابًا (surah AN-NASR/3);
Then exalt [him] with praise of your lord and ask forgiveness of him, He has ever accepted of repentance».
Answer:
Asking for Allah's forgiveness is of different ranks, And everyone asks for God's forgiveness according to his own rank and level. One seeks forgiveness because of committing the sin, the other pray for forgiveness because of doing some the detestable acts and some others may beg for forgiveness because of thinking of the sin, but some special people ask for Allah's forgiveness just because of their involvement in necessary worldly affairs such as eating and sleeping instead of having a proper spiritual connection to their lord.
The Prophet (peace be upon him and his household) asks for Allah's forgiveness, but not due to committing the sin, and not even due to the thinking of the sin, rather, because he thinks that he has not worshipped Allah in a way which Allah (J) deserves. [1]
Note:
[1]: Nahjul Balagha, p. 159