Why is "son of an Israelite woman, whose father was an Egyptian" called that way?

Question

Leviticus 24:10 "Now the son of an Israelite woman, whose father was an Egyptian, went out among the children of Israel; and this son of the Israelite woman and a man of Israel fought each other in the camp."

If it can indeed be derived from this verse that the son of a Jewish woman and a gentile father is indeed Jewish, then why does the verse mention "son of the Israelite woman and a man of Israel" rather than "two men of Israel"? And why is it that he is called "the son of an Israelite woman, whose father was an Egyptian" instead of simply "Israelite man"?

Doesn't that indicate that instead, there is a difference between an israelite and someone who is the son of a gentile father? Also, doesn't the fact that "went out among the children of Israel" is mentionned mean that the son of a gentile father is initially not "among the children of Israel" and thus not an israelite?

A few verses later the following is mentionned: "The sojourner as well as the native, when he blasphemes the Name, shall be put to death." why is "the sojourner" mentionned in this context, as if the son of the Egyptian father was not a native (an israelite)?

Considering all this, it seems obvious to me that he wasn't considered an israelite, or at least not fully?

Answer 1

The Ramban explains that it teaches us that he is Jewish but has no inheritance in the tribal land allotments, because those are along the paternal line.

Answer 2

The son of Israelite woman according to Rashi on Vaikra 24:10 quoting Midrash Tanchuma 24, was a son of the man killed by Moshe in Egypt. That man (see Rashi) raped Sh'lomis bas Divri and was making fun of her husband. Furthermore, Rashi states there, quoting Sifra / Toras Kohanim, Emor, Section 14:1 that the son of Israelite woman converted. In other words the word "sojuorner" means a convert, and the verse Vayikra 24:22 states that the law is the same for a convert and for a born Jew.

There is an argument between Ramban and chachmei Tzarfas (Chizkuni) on Vayikra 24:10 about when the giyur of the son of Israelite woman took place, prior to Sinai or after Sinai, as well as other conversion implications as discussed in Ramban and here (Thanks Nahum). The French Rabbis (chachmei Tzarfas) stated that prior to Sinai, being Jewish required having a Jewish father and not necessarily a Jewish mother. In other words, son of the Israelite woman lived as an Egyptian, he was not circumcised (1), and he had to convert after Sinai, even though he had a Jewish mother and the law regarding inheriting Jewishness shifted from father to mother.

Ramban says that prior to Sinai both parents needed to be Jewish, but since the boy followed his mother he converted in Egypt.

Ramban explains, that the desert travels required that the Jewish people organize under degalim (banners) in camps based on the lineage from their father. (2) The group of converts followed the Jewish camps but they did not enter the camps. The son of Israelite woman did not want to follow the rules that everyone else did.

There were additional differences between the converts and the sons, who had a Jewish father regarding inheritance of the land in Eretz Israel but they were not relevant to the problem that arose between the son of Shlomis bas Divri and the people from shevet Dan.

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(1) There is a comment from Vilna Gaon regarding the plague of lice of why it did not impress pharaoh. According to him, the son of the Israelite woman has lice, although he lived among the Jews. Other Jewish people did not have lice. Nevertheless, because this man had it, pharaoh hardened his heart.

(2) In fact, one of the reasons why inheriting Jewishness shifted from father to mother was because Jewish women in Egypt sacrificed themselved to bring children of the 12 Sh'vatim, when they could have children with men of other nations.