Qitzur Shulchan Arukh – 181:21
A witness who is related to one of the litigants or of the judges, or the witnesses are related to each other, even if the relationship is via their wives [ie only related by both marriages], there are times when they are disqualified from testifying. Even if they are related only to the cosigner and now the borrower, they are also disqualified from testifying for the borrower.
This is because the Torah disqualified the testimony of relatives not because there is a presumption that they love each other, for they are disqualified from testifying whether on his behalf or to his obligation. Rather, it is a decree of scripture. Even Moses and Aaron would not be kosher for testifying one for the other. Therefore, any witness who has any relationship to one of those mentioned, or was related and is now distant [e.g. after a divorce that used to connect them] and the judges don’t know [of the relationship], he is obligated to inform them, and they will tell him whether according to the Torah there is sufficient reason in this relationship to invalidate him [as a witness in this case] or not.
The Qitzur is clear that this law is not due to the logic of the situation, but is simply followed because the Torah said so. And this is why the judges can’t decide the witness is reliable despite any family connection. Still, I am inclined to find a lesson we can take from this verse. Keeping in mind that even if it were known for certain that I were correct, it would not influence the law. Like in science, theory about the meaning of a halakhah is subject to fitting to the evidence of the halakhah itself, and not the other way around.
The invalidity testimony of relatives is different than the rule that a person can not incriminate themselves — ein adam meisim atzmo rasha. This doesn’t mean, as in US law, that he has the right to remain silent. But more than that — even if he didn’t, and said something self-incriminating, the testimony is stricken. More so, sometimes it is split: If someone says that they stole livestock, we accept his testimony with respect to his owing the money, but not with respect to any extra penalties related to theft. However, here the relative can not even testify that the money is owed due to an honest transaction.
It would appear, though, that this difference is due to another factor. “Shavei alei chatikhah de’issurah” — he placed upon himself a portion of prohibition, or if it’s a fiscal case, a person can voluntarily assume a debt. However, this is perhaps as a personal commitment, not via the usual concept of credibility. It makes no difference if the person is lying, since a pledge is binding anyway. So, perhaps in terms of credibility, a person isn’t believed as an aspect of this law. Adam qarov eitzel atzmo — a person is their own relative.
This would imply that the reason for not believing someone who incriminates himself is not similar to America’s Miranda Rights, which are designed to remove the motivation for the legal system to extract confessions in immoral ways. Because in terms of credibility, the halachic rule goes beyond criminal law.
I would like to suggest a more general theory, one that includes the case of a relative, the litigant, as well as why women can not testify in cases of money or where one is determining whether a punishable sin was committed. They are believed with respect to defining the status of an object or situation before anyone may have sinned because of it. And if subsequent to the court determining that a given food was prohibited based on a woman’s testimony, someone did eat it, he would be punished. (As at the time of her testimony, it was not an issue of sin, but of abstract prohibition.)
So, it would seem that the testimony of a woman is not problematic from a credibility perspective. Then what is it?
Perhaps, the problem is that a judge can’t assess the testimony of someone whose relationship to the case is too different than his own. And thus, one of the litigant’s testimony may well be true, but the judges are ill equipped to make that determination. Similarly, that of the person himself are not believed, as we see from the guilt implication of those words — barring the issue that his words could be taken as accepting personal obligation even if he were lying, and therefore they are binding anyway. Last, a woman can not serve as judge, therefore there is an inevitable gender gap when cross examining her testimony. And so, in any case where cross-examination is obligatory (or may later become obligatory, such as the witness to a wedding where the marriage might later become a matter of doubt), her testimony is not accepted.