Introduction This mishnah teaches that a get must be written with the express intention to divorce the specific woman to whom it will eventually be given. This rule is derived from a midrash on Deuteronomy 24:1, “And he writes for her”. The words “for her” are interpreted to mean that the get must be written specifically for her. Our mishnah will illustrate this principle.
Any get which is not written [expressly] for the woman [for whom it is intended] is invalid. How is this so? This mishnah introduces the halakhah mentioned in the introduction, according to which a get must be expressly written for the woman who will be divorced with it. The rest of this mishnah will illustrate this principle.
If a man was passing through the street and heard the voice of a scribe dictating “So-and-so divorces so-and-so from such and such a place” and he says “that is my name and that is the name of my wife”, it is not a valid [document] with which to divorce his wife. In this scenario, a scribe was teaching his students to practice writing divorce documents. These documents were probably always written by scribes, as they require great skill and precision. A man walking by heard the scribe and noticed that the names being used matched those of his and his wife. It dawned on him, wow, I could use this to divorce my wife (I believe that this is intentionally humorous, so you are permitted to chuckle.) The document was only for practice and was not written to be used at all, and therefore certainly cannot be considered as having been written for a specific woman.
Moreover: if he wrote [a get] with which to divorce his wife and changed his mind and a person found him and said to him, “My name is the same as yours and my wife’s name the same as your wife's”, it is not a valid [document with which the second] may divorce his wife. In this case, the document was written to be used to divorce, but not to be used by this husband to divorce this wife, but rather for different people who happen to have the same name. Since it was not written for this man’s wife, he may not use it, even though the names are appropriate.
Moreover: if he had two wives with the same name and wrote a get with which to divorce the elder, he may not use it to divorce the younger. In this case, the correct husband wrote the get, but he wrote it with the intention to divorce one of his wives and now he wants to divorce the other. Since the get was not written to be given to the younger wife, he may not use it to divorce her. As an aside, you can imagine how interesting family life must have been for the family in which a husband married to two women with the same name! If you think Jacob had problems with Leah and Rachel, think of this family. (Again, I think this is supposed to make you crack a smile, so feel free).
Moreover: if he said to the scribe, “Write [a get] and I will divorce whichever I choose,” it is not a valid [document] with which to divorce his wife. Finally, a husband cannot tell a scribe to write out a get, leave the name of the woman blank, and then the husband will later decide which wife he wishes to divorce. In this case, the “correct” husband wrote the get, and he did not actively intend to give it to a different wife. Nevertheless, the positive intention to give it to a specific wife is lacking and hence the get is invalid.