The Torah calls the divorce document Sefer K’ritut, literally “a document of cutting off” (Deut. 24:1). For some reason the document is known as a gett.
There is a grammatical explanation which I heard from Professor MD Goldman of Melbourne University; the Talmudic Encyclopedia quotes it in the name of the K’hillat Ya’akov of Rabbi Ya’akov Algazi.
This view says that in Hebrew linguistics the letters gimmel/tet never come in that order, and if anyone tries to unite them the union cannot be sustained. Sometimes two human beings cannot sustain a marital union and need to be separated by a gett.
The Targum Onkelos renders sefer k’ritut into Aramaic as gett p’turin, a deed of dismissal, so sefer in Hebrew and gett in Aramaic may be saying the same thing. Perhaps the word gett may be from the root ch-t-t, to engrave.
If we move from the academic to the human issue, it is important to note that most people who go through the difficulties of divorce are far from giving up on the institution of marriage as a whole. Almost all embark on a marriage to a new partner.
The first marriage brought its disappointment and tragedy: older and wiser, the divorcee is far from being defeated. The divorce statistics are not the whole story.