The adversarial process is an extension of the right to be heard. Each side in any legal proceedings is entitled to lead the evidence and make the submissions it chooses. Just as the market efficiency relies on the self-interest of every trader, so the adversarial system relies on the self-interest of every litigant to put before the court the evidence and arguments necessary to reach a just outcome.
When a judge cross-examines witnesses or postulates from the bench during the trial on the credibility of pleadings or witnesses, it creates an impression of bias and an incentive for the judge to pre-judge the matter, before hearing all the evidence, in order to prove himself right.