In the early years of Henry VI's reign there is nothing to suggest that Richard, Duke of York was anything but a loyal subject, or that anyone thought otherwise. So what changed?
In the first part of the reign English politics were dominated by the King's uncle, Humphrey, Duke of Gloucester and great-uncle, Cardinal Beaufort. (These two heading - in simplistic terms - the 'war' and 'peace' parties respectively). Both treated York with due respect and he performed whatever duties he was allocated without any obvious fuss.
One factor leading to York's disillusionment with the regime was undoubtedly the increasingly chaotic financial situation. This impacted on him indirectly - by limiting the resources available to him as a commander in France - and directly by increasing the government's debt to him in respect of war wages and other fees to an insupportable degree. Even a landowner as rich as York could only tolerate this for so long. Eventually he was forced to pawn his jewels and even parts of his estates to make his books balance.
The second factor was the replacement of Gloucester and Beaufort in the King's counsels by the like of William de la Pole, Duke of Suffolk and Edmund Beaufort, Duke of Somerset. These men favoured peace with France, whereas York inclined more to the war party. More importantly, they effectively excluded York from the King's counsels and got their grubby hands on what little money and patronage was available.
Politics is always ultimately a dispute between those with power and those without it. It's also quite common for the 'outs' to claim that the 'ins' are corrupt and incompetent. In the cases of Suffolk and Somerset there was perhaps more truth attached to this claim than is usual. (Though it would have taken remarkable leadership to square the financial and military circles we are talking about.)
The separation of York from the inner circle of power led to a growing, mutual distrust. Who 'started' this is hard to discern. York would certainly have argued that Suffolk, Somerset, and later Queen Margaret had the King's ear and told him lies about York's intentions, thus alienating Henry from his loyal cousin. On the other hand, Suffolk, Somerset and the Queen did
have reason to be wary of York. He was the obvious (if not only) 'alternative' government and, given the detail of his family tree, might even be put forward as an alternative sovereign. The country was not stable, and those in power must have feared a 'revolutionary' situation arising, after the example of the falls of Edward II and Richard II.
York's claim to the throne (in the event of Henry's death) had been talked about in Parliament, a destabilising factor in itself. York's readiness to take up arms in 1452, and then again in 1455, demonstrated that the doubts and fears about his loyalty were not completely groundless. Though York was successful in 1455 (mainly thanks to the Nevilles) it's fair to say that the bulk of the nobility remained loyal to Henry despite the ineptitude of his government.
York's justification - that he took up arms only because he had failed to get a hearing by 'constitutional' means - is also not unreasonable. As the leading peer he had, in medieval terms, the right to be one of the King's leading advisers. Henry's decision to exclude him from this role, and his undue preference for the likes of Suffolk and Somerset, was bound to lead to trouble.