Another one of the differences between dinei mamonot (monetary cases) and dinei nefashot (capital cases) that is taught in the Mishna (32a) is that in dinei mamonot anyone can step forward to offer evidence on behalf of either party, but in dinei nefashot we will allow anyone to speak on behalf of the accused, but not against him.
The Gemara suggests that this follows the opinion of Rabbi Yosei bar Yehuda who learns from the passage in Sefer Bamidbar (35:30) that a single witness cannot testify that a person should die, but he can testify to allow him to live. The Sages, on the other hand, believe that we will not accept any statement from the witnesses beyond their testimony, even if they want to speak on behalf of the accused. Reish Lakish explains that the Sages will not let the witness offer any statements beyond his testimony, because it would appear as though he is biased in his testimony.
The Meiri explains that it is possible that we are concerned that the witnesses are worried that the family of the accused might threaten them, if he is found guilty based on their testimony. Other explanations include the possibility that the witnesses are worried that someone may come and accuse them of being false witnesses.
The Sages understand that the passage in Sefer Bamidbar refers to a student who is listening to the case being argued and wants his opinion to be considered in the decision, as well. According to this approach, the student would be listed too only if his suggestion would help the accused, but not if it would damage his case. The Ran points out that we listen to any argument that is put forward in the courtroom – even if it comes from the defendant or the plaintiff, and certainly if it comes from an objective observer. The Gemara’s intent must be to limit the student’s participation regarding the possibility of including him as a member of the court, which we will only do if he is arguing on behalf of the accused and not if he is against him.