The purpose of the ICC is to bring war criminals to justice when their governments refuse to do so.

Now, even in our judiciary system, there are problems about deciding who can bring a decision. For instance, a judge in a famous criminal paedophile case in Belgium was successfully dismissed by the defender's lawyers because he had a dinner with the parents of the victims.
If a judge is related to one of the sides, he's going to be suspected of favoring one side and loose objectivity.

About accountability of an international institution like the ICC and the origin of lots of its members.
Well, they're probably not elected for life, and there's a large number of them, from all kinds of backgrounds. They have one thing in common: they're all very competent in law and preferably international law.
It is also entirely possible a judge from a non democratic country can very well be competent to judge a case between a democracy and a dictatorship that don't share his religion or are from the other side of the globe.
The judges cannot be accountable to their own countries but to their employer, the international institution. It's like the EU commissionners who have to regulate trade issues: they often have to rule against companies from their own country. If it's obvious they favor their own country or an individual from their own country, they face charges. It happened to Edith Cresson. The point is: they're not alone and everybody knows what everyone else does.
It's not a perfect system, but sometimes international organizations are needed because we live in a complex world with countries with very different governments.

Raoul