Why does the "pale young gentleman" challenge Pip to a fight. What is his reason for being at Satis House?

He actually gives no reason. The closest he gets is found in the quote below. We aren't given an exact reason for his presence, but we do know that he was studying and had ink on his hands.

"Stop a minute, though," he said, wheeling round before we had gone

many paces. "I ought to give you a reason for fighting, too. There

it is!" In a most irritating manner he instantly slapped his hands

against one another, daintily flung one of his legs up behind him,

pulled my hair, slapped his hands again, dipped his head, and

butted it into my stomach."