Why does the litigant accept the oath of his opponent in lieu of payment? Doesn't he himself claim that his opponent is a thief, such as in the case of two people with a garment, and just as he claims that his opponent lied about money, he can suspect that his opponent will take a false oath?

That argument however is false. There are people who will withdraw from taking a doubtful oath, but will not withdraw from taking doubtful money. And what is the reason for this difference in attitude? Money taken improperly can be returned, but an oath once uttered cannot be recalled.