Duryodhana was the son of a king and should be made the next king but still generally all people consider Yudhisthir to be the righteous owner of the throne. Why should Yudhisthir be the crown prince when Pandu and his wives had already left their kingdom and appointed Dhritarashtra as the king. Also, Yudhishthir was not a direct son of Pandu. Pandu himself was not the righteous owner of the throne. He got the throne because Bhishma said that Dhritarashtra will have problems due to his blindness, but later on also he became the king. So, it was Dhritrashtra right to be king and later on he became the king and therefore rightful owner to succeed him should be Duryodhana. I think if there was no such confusion as to who should be the king between Yudhisthir and Duryodhana, then there wouldn't have been any Mahabharata.
In Bharat dynasty (in which Yudhishthir and Duryodhan were born), it was not necessary that only the eldest son of a king will become the next king. The one who was worthy of becoming a king used to be choosen. Even king Bharat himself didn't appoint his son as his successor even though he had 9 sons.
Yudhishthir was best choice for the king because
Yudhishthir was more worthy of becoming a king than Duryodhan in the opinion of Dron, Bhishm, Vidur, Krip and the citizens. Hence, Yudhishthir was choosen as Yuvraj (successor of the king).
But later evil Duryodhan tried to kill Yudhishthir and his brothers in laxagrah with their mother. And
Only on the false news of Yudhishthir's death in laxagrah, Duryodhan was choosen as Yuvraj.
By birth neither Duryodhan nor Yudhishthir had a right on the throne because technically neither Duryodhan nor Yudhishthir was Kuruvanshi (Kaurav), a new name of Bharat dynasty after king Kuru. Because king Shantanu had three sons Bhishm, Chitrangad and Vichitravirya; Bhishm was bhramchari and other two died before producing any child. By the grace of Vedvyas, all three Dhritarashtr, Pandu and Vidur were born after death of their father Vichitravirya. However, by the grace of Gods (Dharmraj, Indra, Vayu, Ashvinis), all 5 pandavas were born in front of their father Pandu.
By birth, only Bhishm had right on the throne because he was the only Kuruvanshi (Kaurav) at that time.
This was the initial conflict and mostly politics up until this point in my opinion. Reason for Mahabharat was not just this conflict of interest, this was a starting point, yes, but this was not the entire reason.
Duryodhan started to get antagonized after he insulted Draupadi and had Pandavas exiled. This not only earned pandavas more sympathy, but also more credibility for living as laymen in exile. Having Krishna on their side didn't hurt them either.
Duryodhan may have been in line of inheritance, but his actions made him unsuitable (not to mention unpopular) choice to be king.
Very much well posed question. If we step back a few years we will see that the doubt of "who will inherit the throne" arose just after Duryodhana was born.
Question no. 1: Who could question the inheritance of the King's son?
Ans: He/They have to be someone holding similar power (if not less) than the king (Dhritarashtra) himself. Now, here we sense a bit of politics. So, the threat - that someone else (obviously, Yudhishthira) was going to claim the throne in future - persisted from the very beginning. Quite naturally, Dhritarashtra, the King, and also his son Duryodhana would not like it.
Question no. 2: Why couldn't the all-powerful king reject Kunti with her five juvenile sons' plea for asylum in the kingdom?
Ans: The reason is again the same. It is quite sure that a had conspiracy cropped up and the king could do nothing to check it.
This answers the Question.
Selection of the heir was beyond the scope of Dhritarashtra.