A biggest quality of king that he should take care of all citizens with care and selflessly he should not be partial
Supposed if duryodhan become king then would duryodhan have taken care of pandav ? Will duryodhan after becoming king stop enimity with pandavs and give them all basic facilities .
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Would have not duryodhan partial to pandav if he become king.
So if duryodhan become king he would have partial
Lack of tolerance . Indeed duryodhan has lack of tolerance for small small things he invited war even try to kill
So if had become king then for small small mistakes he would given harsh punishment
So to become king one should able to give right and proper justice
And duryodhan was unable to give right and proper justice b
And duryodhan who was always revenge full did himself so many wrong thing uncessary enimity with pandav ( in fact pandav never claims for throne but still he did wrong thing with them many times)
So how duryodhan was position to punish the wrong things when he himself did wrong things
If duryodhan want to become king then he should proove it by doing noble deed by helping praja instead of harming but he never help any praja
But only thing in mind that too destroy pandav
. If duryodhan want he could have utilized his time in welfare of hastinapur and later duryodhan would have king of hastinapur and yudhistar would have king of indraprasth
But duryodhan decided to take meaning less revenge from pandav for small things