Mishnah: One who writes two letters, whether with his right or left hand [has violated Shabbat]
Talmud: It sits well that one who writes with his right hand be condemned [as having violated Shabbat], since this is the normal manner of writing. However, why account the left hand so? This is not the normal way of writing! Rabbi Yermiah said, "The Mishnah speaks of a case of a left-handed person."—For his left hand is like the right hand of the rest of the world.
I have mentioned previously that the thirty-nine Torah-prohibited categories of labor (the avot melakhot) assume their meaning based on conventional definitions of the act they describe. For example, though cooking is prohibited as one of these thirty-nine categories, frying an egg on the hood of a car on a hot summer day would not be a Torah-prohibited act, since people do not conventionally define this as an act of cooking.
In our mishnah above, the act of writing is defined. First, since there are no Hebrew words of a single letter, writing is restricted to the production of at least two characters. No controversy here. Next the mishnah states that writing is defined as such whether it is produced with the right or the left hand. Here the Talmud objects: If a right-handed person writes with his left hand, this is not the conventional manner of writing! Indeed, this is very similar to the case of the egg mentioned above, and should logically not be considered a Torah-prohibited act.
Rabbi Yermiah resolves the problem by reading the mishnah closely: one has performed the prohibited act of writing whether writing (in an ongoing way) with the left or right hand. A left-handed person, though a minority, still remains a full member of human and Jewish society, so that person's act of writing is still conventionally held to be an act of writing. Though they behave differently when they pick up the pen, they are expected to grasp the Torah just as tightly as those who hold it in their right hands.