I have always seen the WORs as a thoroughly mutual event, because the
beginning, middle, and end of the conflict were equally influenced by
Lancastrian and Yorkist maneuvers, incompetence, and intrigue.
Obviously, the seeds were planted at the end of the
14th century (1399) when Henry Bolingbroke (Henry IV) usurped and
deposed his cousin Richard II, which resulted in him facing problems with his own son (Henry V) who was widely rumored to be
planning to do the same thing to him – after all, once you start the
tradition of dethroning kings, where does it end? Then Henry V had the
great success of the Battle of Agincourt (1415), which made it look like
England was going to actually reclaim the French territories they had
lost way back with Bad King John, at the height of the Hundred Years War
(which was started by Edward III pressing his claim to the French crown
through his mother Isabella of France). But Henry V didn’t last too
long – he ruled from only 1413 to 1422, whereupon he died young and left the future Henry VI as a baby less than a year old. This meant a very long minority, which was historically bad news. Henry V’s widow, Katherine de Valois, later remarried Owen Tudor, which was to end up being important, but the end result was that you had first many years of the king being a minor, and then when he did grow up, he was, to put it mildly, not that good at his job. He had a strong saintly streak and was some sort of mentally ill, as evidenced by his numerous complete psychotic breaks. None of this was helped by the fact that his wife, Margaret of Anjou, was the historical personality that Cersei Lannister is based on – aggressive, assertive, manipulating, unpopular, and widely viewed as the actual ruler in place of Henry. Also like Cersei, everyone was pretty darn sure that her son, Edward the crown prince, wasn’t Henry’s – possibly due to the small fact that Henry was off in la-la land when Edward was conceived. Edward, for his part, was likewise the person that Joffrey is based on. He was a teenage prick with a sadistic streak and nobody was that thrilled about the idea of him being king. In short, you now have a huge problem for the Lancastrians: the king is totally useless, the queen is hated, the crown prince is probably illegitimate and an asshole to boot, and England in the fifteenth century is dealing with social unrest and economic upheaval. When this happens, fingers get pointed.
Meanwhile, the Yorkists showed up to remind everyone that they’re actually the real heirs to the crown, that the Lancastrian dynasty was having problems because Henry IV stole the throne, and so forth. Because of the clusterfuck described above, they had a lot of support, and Cecily Neville, the wife of Richard, Duke of York and mother of the future Edward IV, was likewise an influential mover behind the scenes. It wasn’t too long before the Yorkists decided to openly pursue their cause, and a few years of batting back and forth eventually turned into outright war. Richard was killed in 1460, whereupon he had his head hacked off and a paper crown nailed to it to mock him, but it turned out that this wasn’t such a good idea, because it pissed his son (Edward IV) off a great deal and led to the Battle of Towton (1461) which is still, to the best of my knowledge, the bloodiest battle ever fought on English soil – the casualties were so ruinous that something close to 1% of the entire English population died there. In any event, it resulted in Henry VI being deposed and Edward being crowned, and as he was young, handsome, popular (especially with apparently all the women in England) and brought, at least at first, much-needed reform and order to the monarchy, everyone was initially just fine with it. But since Edward fell madly in love with the commoner Elizabeth Woodville and decided to marry her instead of one of the European princesses that was expected of him, this ended up causing a great deal of trouble for him. Elizabeth also had a very large family who Edward openly favored and appointed to important positions (and remember, they are commoners, horrifying the rest of the English nobility) which caused more friction.
In any event, excluding a brief episode (1470-71) where Henry VI was restored, deposed again, then famously murdered in the Tower of London, Edward reigned more or less unchallenged (excluding the usually incompetent plots by his brother George, the Duke of Clarence, and the Kingmaker, the Earl of Warwick, who turned on Edward after helping him to the crown) until his death in 1483, when the penultimate episode of the wars began. His young son was acknowledged as Edward V, but this was when his brother, the future Richard III, showed up and… well, let’s just say he wasn’t getting Uncle of the Year awards. There have been all kinds of contemporary attempts to clear Richard’s name, but the historical fact is, and was widely believed at the time, he almost certainly had Edward V and his younger brother killed while they were prisoners in the Tower. Richard III was not the hunchbacked villain of Shakespeare, and made several attempts at being a good king once he was crowned, but it was undercut by the fact that he was, you know, a guy who had killed his preteen nephews in order to step over them to the succession. This opened the door for Henry Tudor, son of Margaret Beaufort (heiress to the senior line of the Lancastrian claim descended from John of Gaunt, third son of Edward III) and Edmund Tudor, Henry VI’s half-brother (remember Katherine de Valois remarrying Owen Tudor?) to gather supporters in France and sail to England to face Richard. They met in the Battle of Bosworth Field in 1485, where Richard was killed and Henry became Henry VII. To unite the feuding claims at last, he married Elizabeth of York, Edward IV’s daughter, and the red rose (Lancastrian) and white rose (Yorkist) were combined to create the Tudor rose.
Anyway, as noted, both Lancastrian and Yorkist were responsible for the power plays. Henry IV deposed his cousin Richard II in the first place (because Richard II had also inherited the throne young after the death of his grandfather, Edward III, and father, Edward the Black Prince, and while he started out well, distinguishing himself in his handling of the Peasants’ Revolt in 1381, he never recovered from the idea that his subjects had presumed to challenge him and got more and more bizarre and imperious). Then Henry V died young, Henry VI’s insanity and Margaret of Anjou’s intrigues were big problems for the Lancastrians, and hence it was understandable that the Yorkists were able to make a successful play for power, even at very high cost. But once they did have it, Edward IV (the basis for Robert Baratheon) basically spent his time sleeping around and not being hot shakes as a ruler, and Richard III’s method of acquiring the throne made them so reviled that Henry Tudor was able to get his foot in the door. I don’t know that you can say one was wronged more than the other, as it was a combination of numerous political factors and manipulations on both sides of the conflict (as well as powerful women, interestingly). But it did end up producing some of England’s most famous monarchs in the Tudors, and a heckuva lot of great Shakespeare, so there’s that.