One of the exclusive names of Yudhishtira is Ajāta śatru (अजात शत्रु).
Ajāta śatru = Who has no enemies.
Why is he called as Ajāta śatru. Kauravas are his enemies. Aren't they? Why is the name exclusive to him?
While narrating the Mahābhārata, Vaiśampāyana explains how Yudhiṣṭhira acquired the epithet Ajātaśatru. But he may have acquired it before the Rājasūya quest when his kingdom was limited to Indraprastha and its surroundings, because when you start conquering kings and their lands you will inevitably make new enemies like Jarāsandha.
For Yudhishthira, that foremost of all virtuous men, always kind unto his subjects, worked for the good of all without making any distinctions. Indeed, shaking off both anger and arrogance, Yudhishthira always said,--Give unto each what is due to each,--and the only sounds that he could hear were,--Blessed be Dharma! Blessed be Dharma! Yudhishthira! conducting himself thus and giving paternal assurance to everybody, there was none in the kingdom who entertained any hostile feelings towards him. He therefore came to be called Ajatasatru (one with no enemy at all). The king cherished every one as belonging to his family...
According to Monier-Williams dictionary, a few others also had this title.
mfn. (/ajāta--) having no enemy
mfn. having no adversary or equal (Indra), RV.
m. (us-) Name of Śiva-, of Yudhiṣṭhira-, of a king of Kāśī-, of a son of Śamika-, of a son of Vidmisāra- or Bimbisāra- (contemporary of Śākyamuni-)
(Most of this is same as Rakesh's comment, with a tiny bit added)
That name has more to do with Yudhishthira's perspective, of not seeing anyone as his enemy, rather than others not seeing him as enemies. He fights them purely on the basis of dharma, to establish a government/kingdom which rules according to dharma, and not because he feels enmity towards them. The same is not true for Kauravas, who denied Pandavas the simple request of just 5 villages to govern. Or the rest of the Pandavas, who also feel a certain level of enmity towards Duryodhan and others.
Yudhisthira alone is firmly and completely established in dharma, and therefore is called ajata satru, not seeing anyone as an enemy.
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