Henry Tudor was a direct legitimate descendant of John Gaunt, who is a primary figure in the Lancaster line, and he was presented as a Lancaster candidate. He also married a York, Elizabeth of York. So his line unified the two cadet branches of Plantagenet. Why isn't the house of Tudor considered a cadet branch of Plantagenet/York/Lancaster?
Henry's descent from John of Gaunt was matrilineal. All of the "Plantagenets" (up to the last survivors, the children of George, Duke of Clarence, Elizabeth of York's uncle) were descended from Geoffrey, Duke of Anjou through the male line.