Why are there an uneven of servers in each data center?

[Malzian]

And why can't people in the same data center play with anyone outside of it?
Is this a design choice?

Yes, that is the entire reason for Data Centers existing.

Weeeell.... Yes and no. The datacenter split is by design, yes, but not to intentionally to keep players apart per-say. It's more a matter of the implementation of the duty finder and the instance servers.

See, here's the thing... Let's say you have a group of players, whatever size... do the math thing and say that it is a pool of size n. If you have 4 players and you need to choose 4, then it's simple, you have 1 choice. If you have 5 players and need to choose 4... you now have 5 that you can make (order doesn't matter so a number of duplicates can be eliminated). 6 players... 15. 7 players... 35. To bring it to what you're more likely to encounter... 1000 players is 41,417,124,750 possible combinations to make a party of 4 players. For 8-man content the number is even worse. Then you need to make sure that you have the right combination of roles to do the content...

To cut down the time needed to perform the matching, SE needed to split the populations to be chosen from down into manageable chunks. Yes, not all players on all datacenters will be playing at the same time, nor will they be competing to get into the same duties, but even at 100 people the number of combinations is close to 3 million. By pure terms of computing power required to run this algorithm efficiently you wouldn't want to take, say, the several million that are currently subscribed and throw them all into the same pool. You'd never get a party again.

Also, to head this off, yes there is the option of 'first come, first served', but even that runs into the problems of having to find all the people looking for the same content at the same time and formulating a valid party by popping people out of the queue. Still a process that becomes more problematic with the more people you throw into it.