Question: why does griphook want the sword of gryffindor?
Answer: The sword of Gryffindor was made by Goblins for Godric Gryffindor and as per their notion of ownership now that Gryffindor was dead it should come back to the descendants of the goblin who made it. Hence Griphook wants it desperately as he feels he is the rightful owner of the sword.