It's pretty obvious right from the start that Draco displays many of the same traits as Harry's cousin Dudley. In their first encounter he shows that he is selfish and spoiled. On top of that he insults Harry's newfound friend Hagrid and shows a contempt for muggles:
‘That’s Hagrid,’ said Harry, pleased to know something the boy didn’t. ‘He works at Hogwarts.’
‘Oh,’ said the boy, ‘I’ve heard of him. He’s a sort of servant, isn’t he?’
‘He’s the gamekeeper,’ said Harry. He was liking the boy less and less every second.
‘Yes, exactly. I heard he’s a sort of savage – lives in a hut in the school grounds and
every now and then he gets drunk, tries to do magic and ends up setting fire to his bed.’
‘My father’s next door buying my books and mother’s up the street looking at wands,’ said the boy. He had a bored, drawling voice. ‘Then I’m going to drag them off to look at racing brooms. I don’t see why first-years can’t have their own. I think I’ll bully father into getting me one and I’ll smuggle it in somehow.’
Harry was strongly reminded of Dudley.
When they later meet on the train he insults Harry's new friend Ron, openly displays arrogance towards other wizard families and he has two thuggish looking "bodyguards" on either side of him:
‘You’ll soon find out some wizarding families are much better than
others, Potter. You don’t want to go making friends with the wrong
sort. I can help you there.’
He held out his hand to shake Harry’s, but Harry didn’t take it.
‘I think I can tell who the wrong sort are for myself, thanks,’ he
Within seconds they're nose-to-nose getting ready to fight.