So arbitration is not an adversarial proceeding?

No, it is still an adversarial proceeding, in that there is one side presenting its views, with the other side countering and presenting its views, and both hoping that the arbitrator will decide who is right and who is wrong. An arbitration tends to be less adversarial than a trial, but it is not without contention. The reason it seems to be less adversarial is because of the more relaxed procedure and the more involvement by the spouses.