well, what do you expect? if you behave like a twit, you get treated like one.
northumbria is an english region. in a feudal architecture, the earl of northumbria had to pay homage to an english king. the king of scotland could not. so of course he had to accept the loss of the earldom.
instead he rebelled against henry ii over an english possession and paid the price. henry obviously couldn't accept the annexation of northumbria. and he had the force to protect his domain.
but of course, by rebelling, william revealed his character and intentions. faced with a neighbour who was likely to invade if given the chance, henry restricted his ability to do so.
scotland was a pugnacious neighbour during this period. in this case, william carefully placed scotland under henry's heal. genius.