I was reading throught the book of judgement and it states that all arbites are recruited from the schola progenium? how does that work when in character creation you can choose any background for the arbites, am i missing something?

I'd just say that the Schola Pregnium is just one of the sources for recruits into the Arbitaries, although its possible that fluff-wise Arbitaries from the Schola may come better equipped than most and have a higher procentage of their numbers in high posts than their procentage of the total numbers may hint at.

A few things:

1. Arbitrator the class does not equal Arbitrator as a member of the actual Arbites:
Its more of a generic law enforcement related class. Yes it does have a few lores tied into the Arbites, and that has to do with how the Arbites are kind of the blanket law enforcement agency of the Imperium. An Arbitrator (of the class) could just as easily be a planetary enforcer.

2. Home world as a character aspect has more to do with what has actually shaped you as a character, and less about what specifically occurred to you.

Yes, you might have gone to the Schola, but your time in the hive city is what really shaped you as a character.

Yes, all "cookie cutter" members of the Arbites have been trained in the Schola. Obviously, player characters being the special snowflakes that they are, this does not 100% need to be the case. Also remember, Arbites quite specifically do not serve on their home world, so as to be impartial.

I see the back ground you choose for your Arbiter could be the most resent one. Meaning you went to the Schola but the hive world is what shaped them. makes since. thank you.

Some people were raised from childhood in Schola Progeniums (typically the orphans of Imperial military officers); other were born and raised on different types of planets, and attended the Scholas only for a few years of advanced education. At least, that's how I interpret it…