Why did Imam Ali (PBUH) not reclaim Fadak during his caliphate?

Answer

In the name of Allah, there could be many reasons for that. One of them is that the first and second caliphs claimed that they had placed Fadak for the benefit of the general Muslim public. The third gave it to some of his relatives, which provoked anger among the Muslims. So, had Imam Ali (PBUH) reclaimed Fadak and given it to himself or his children, the ignorant might have imagined that he followed the same path as the third caliph. It is also possible that the secret behind not reclaiming it lies in the statement of Lady Fatima al-Zahra (PBUH) to Abu Bakr when he insisted on not returning Fadak to her. She said: "Take it..." and then said: "You will meet him [the Prophet] after your resurrection and judgment, where Allah is the Judge and Muhammad (PBUH) is the opponent—there, the wrongdoers will be the losers." (paraphrased meaning). Another possible reason—hidden from us—was hinted at by Imam Ali (PBUH) when he was asked why he did not take back Fadak. He replied, in meaning, that the claimant and the usurper had already gone to meet Allah, the Exalted. Ultimately, the reason we must believe in is that Imam Ali (PBUH) is infallible; he acts according to what Allah commands him. He indeed acted accordingly, even if we do not understand the wisdom or reason behind it. Allah is the All-Knowing.