Let's get things straight - Jordan isn't a bad person...he just really dislikes being associated with his family. Does he detest his sisters? Maybe. Does he isolate his younger brother? Somewhat. Does he care about his cousins? Not too much. As I said, not a bad person. Most people just see him as hating anyone related to him which, to some extent, is true - but to say he hasn't tried is a different story. For the majority of his life Jordan had tried to love his siblings, tried to be interested in his cousin's activities but they all bored him. As a result of this, there's definitely two sides of Jordan Park.
The side his family sees is very cold, an avid isolationist with a temper that's so short it could snap at any moment. It's very rare he exercises kindness and whatever he says is usually cold and short with not much thought about the feelings of others given. This side of him has gained him the reputation of being the brat of the family. The way his parents view him is just a blackhole that all their money seems to being sucked into. The way Jordan sees it, is that if nobody's going to be proud of him, why should he be proud of them? If nobody can give two shits about him, why should he make the effort? Whichever way you put it, Jordan is not a family person.
The other side, the social side, is the much better side of Jordan. It was first brought out by a certain Everett Kye who to this day remains as Jordan's best friend. Jordan's far kinder in this side, laughing near enough all the time and isn't afraid to add in some sarcasm when needed. He's the definition of a social butterfly...so much so to the point where he has regular one night stands because his confident aura draws people in. As kind as he is to everyone, only a select few get genuine kindness treatment from him. The only one really being Everett at this point. For someone who'd refused to do anything for his family, Jordan would give the world and more to Everett.
One trait, regardless of what side Jordan shows, that is prominent is jealousy. Jordan is an extremely jealous person and little things set him off. You can hardly blame him when his best friend is gorgeous, his sisters are intelligent and quirky and his brother is on his way to being a professional Quidditch player. Not to mention his cousins are probably doing something amazing as well. Yeah, it seems Jordan was destined from the very beginning to be a jealous person. Does he care? A little - though he uses it as a determination to get exactly what he wants.
Byun Tae-Yeon and her twin sister, Mi-Yeon, belonged to the influential Seoul branch of the Byun Family. However influential they were, it was never enough and soon it became apparent that the Park Family possessed more influence than they did or ever could. Coincidentally, the Park Family had twin sons, Ki-Hyun and Soo-Hyun, who both cited the Byun sisters to be their brides. While her sister was less than pleased to be married, Tae-Yeon was head over heels for Soo-Hyun and after they married the two left for England.
In the new country, the couple settled into a home on the outskirts of Wolverhampton, adopting the names Taylor and Samuel respectively. Once settled with high jobs in the Ministry, the couple began to expand their family. First was Phoebe Joohyun, then Chloe Mihyun and then followed by the couple's first son, Jordan Chanhyun. Jordan grew up as the family baby for nearly five years, constantly blabbering to his parents how he'd love a younger brother so he could a.) play with him and b.) so he wouldn't be his sisters' real life Ken doll. His blabbers were answered when he was 4, nearly 5 with his mother giving birth to the final Park child, Finnley Kanghyun.
After that, the siblings - who remained close - broke off into their respective gender pairs and played together. Jordan and Finn often played on the muggle games console their parents had brought, or practised Quidditch in the back garden. While the sisters remained close, as time went on Jordan began to lose his closeness with Finn. It became apparent when Jordan had his first magical experience at 9 years old - making water boil over a saucepan. Ever since then, Finn had tried to be like him and frankly, it irritated Jordan. Soon the older was pushing away the younger until by the time Jordan went to Hogwarts they were disconnected.
Throughout Hogwarts, Jordan continued to try and isolate himself from his family, not wanting to be remembered as Phoebe and Chloe's brother. It was worse when Finn joined - for a year all four siblings were in the same school and they were often bunched together at any chance. Hogwarts is a blurry memory for Jordan - he doesn't want, nor need, to remember it.
He's recently graduated and is excited to begin his own life - mainly living off his parents' wealth.
He doesn't hate them, let's get that out of the way. He simply dislikes being associated with them. What he does hate is being told he's not as intelligent as Phoebe, or quirky as Chloe or as sweet as Finn. He's his own person but in terms of the Park family, he's a disappointment. So as far as he's concerned, the less connected they all are - the better.