The fourth perek of Massekhet Shevuot begins on today’s daf, and – as its name Shevuat HaEdut (The Oath of Testimony) indicates – its focus is on oaths taken in response to a demand that someone testify about something that he witnessed, and he refuses to testify. This law is based on the passage in Sefer Vayikra (5:1).
The Mishna opens by listing who is included in this law and who is exempt from it. Thus, the law applies only to men and not to women, it does not apply to relatives who cannot testify nor to people who are removed from testimony because of forbidden acts that they committed (e.g. if they are robbers).
The rishonim ask why we need a list of people who can and cannot testify, rather than sufficing with a simple statement that the law applies only to people who, theoretically, would be accepted as witnesses in a Jewish court. They explain that there are a number of situations where a person would be allowed to testify based on Torah law, but the Sages prohibited him from acting as a witness. The Mishna needs to spell out cases in order to emphasize that even though they are acceptable on a Torah level, we will not apply the laws of shevuat ha-edut to them since we would not accept their testimony in court.
Rabbi Akiva Eiger points out that there are cases where a woman’s testimony would be accepted in court – e.g. a case of sota. Why don’t these laws apply to a woman who has witnessed something about which she can testify? He argues that the passage in the Torah emphasizes that these laws apply to an ed – someone who is a kosher witness. When a woman’s testimony is accepted in a Jewish court it is because she is a proper witness so much as it is because there are other factors that allow the beit din to accept her words.