Under normal circumstances many people can be just. But Islam commands its followers to be just even in the face of strong conflicting emotions. In dealing with other human beings, two major impediments to justice are love and hatred. See how the Qur'an teaches us to overcome the first impediment when we are dealing with our closest relatives or even ourselves. "O ye who believe! Stand out firmly for justice, as witnesses to Allah, even as against yourselves, or your parents, or your kin, and whether it be (against) rich or poor: for Allah can best protect both. Follow not the lusts (of your hearts), lest ye swerve, and if ye distort (justice) or decline to do justice, verily Allah is well-acquainted with all that ye do." [An-Nisa 4:135]
Here is the resolution from the Qur'an of the perennial conflict between self-interest and justice. Be just, even if it is against your narrowly defined self-interest or of those very close to you. Ignorant people think they are protecting their self-interest by being unjust to others. Their decision to be just or unjust may be based on a cold calculation of self-interest. But real faith in Allah elevates one beyond that narrow-mindedness. These verses remind us that the real protector of interests of all people is also Allah and He will protect us when we follow His command to be just. The justice demanded by Islam permits no favoritism.
The other equally potent impediment is hatred. Here again Qur'an commands: "O ye who believe! Stand out firmly for Allah, as witnesses to fair dealing, and let not the hatred of others to you make you swerve to wrong and depart from justice. Be just: that is next to Piety: and fear Allah. For Allah is well-acquainted with all that ye do." [Al-Maidah 5:8]
In other words you cannot do injustice even when you are dealing with the enemy. The natural, uneducated, and uncivilized tendency is to treat the enemy as less than a human being; one who has no rights and deserves no justice or fairness. It was as true in the pre-Islamic tribal jahilya (based on ignorance) society as it is today. See how Islam directly curbs it. It is a command to the believers, with a reminder that Allah is watching you, that enmity of others cannot be used as an excuse for committing injustices against them.