Final answer:
The Duke of York, Richard, believed his royal lineage was superior to the Lancastrian line because he directly descended from Edward III's second and third sons, while the Lancastrians descended from the fourth son. This, combined with the principles of agnatic primogeniture, made his claim seemingly more legitimate during the time of the War of the Roses.
Step-by-step explanation:
Why Richard, Duke of York, Believed His Royal Lineage Was Stronger Than the Lancastrian Line
Richard, Duke of York, asserted that his claim to the English throne was stronger than that of the Lancastrians due to his direct descent from two significant royal lineages. He was a direct descendant not only from Edward III, through the male line of the Duke of Clarence, Edward III's second surviving son, but also had ties through the female line of Lionel of Antwerp, Edward's third son. The Lancastrian claim to the throne was through Henry IV, who had usurped the crown from Richard II, and as Henry IV was descended from Edward III's fourth son, John of Gaunt, it was seen as a weaker claim compared to Richard of York's descent from the second and third sons. Moreover, internal conflict during the War of the Roses cast questions on the legitimacy of the Lancastrian rule, and with the tragic deaths of his relatives, who were the reigning princes, York's claim by right of kinship was fortified.
These complex dynastic claims were at the heart of the War of the Roses, a series of civil wars fought over control of the English throne, with the Duke of York representing the Yorkist claimants, and the Lancastrians represented by Henry VI and his successors. Richard's confidence in his claim was based on the principle of agnatic primogeniture, which favored male succession and proximity of bloodline, making his lineage seem more 'royal' than the existing Lancastrian lineage on the throne.