The Great Debate
The debate that caused great strife between Yosef and his brothers, involved their status while living in Canaan, before the Torah was given.
The brothers felt that they were already a very distinct Jewish nation. Yosef felt that they were still guests as the Torah was not yet given.
We see this in the explanation regarding Yosef’s speaking badly of his brothers. The Midrash says that Yosef told their father that his brothers were violating אבר מן החי, tearing the limb off of a live animal.
The Rabbis explain that certainly the brothers were not guilty of such a terrible sin. It represented a debate in the interpretation of this law. This law applied to both Jews and non-Jews, and was one of the Seven Noachide Laws.
The rules for non-Jews was more strict than for Jews. This was true of some of the other Noachide Laws. For example, stealing was punishable by death for the Noachide, while the Jew paid a fine.
In this case, a non-Jew must wait until the animal has completely stopped shaking after slaughter, before one can begin cutting up the meat. A Jew can begin the process after Shechita, even when the animal is still shaking, מפרכסת.
The brothers argued that they were already the Nation of Israel, and they followed the latter procedure. Yosef argued that they were not yet the Nation of Israel, and the Noachide Laws also applied to them.
We need to look at our Jewish biblical heroes from different eyes. There is a deeper explanation than that which might even seem like superficial quarreling. All of the brothers knew that they shared a special destiny. They only had some disagreement as to how to get there.