Lévitique 24:10

But a wicked man, a rebel against the God of heaven, had come out of Mizraim, the son of the Mizraite man who had killed the man of Israel in Mizraim, and had gone in unto his wife, who conceived and bare a son among the children of Israel. And while the Israelites were dwelling in the wilderness, he had sought to spread his tent in the midst of the tribe of the children of Dan; but they would not permit him, because in the arrangements of Israel every man dwelt with his family by the ensigns of the house of their fathers. And they contended together in the camp, and the son of the Israelitess with a man of Israel, who was of the tribe of Dan, went to the house of judgment;

The son of an Israelite woman came out from his tent. Compare, “they came out and stood at the entrance of their tents” [Numbers 16:27].

the son of an Egyptian man who had converted to Judaism.

[the] Israelite man Scripture omits the definite article before the modified noun, as in “to [the] rich man” [II Samuel 12:4] and “[the] seventh day” [Genesis 2:3]. There is no known reason why the upcoming passage is included here. Perhaps the blasphemer spoke inappropriately regarding the showbread, or the oil, or the sacrifices.

AND THE SON OF AN ISRAELITE WOMAN, WHOSE FATHER WAS AN EGYPTIAN, WENT OUT, etc. This means that he went out among the children of Israel, (and he went out) is not adjoined to the phrase, among the children of Israel. Ramban thus calls attention to the fact that they are to be understood together: “and there went out among the children of Israel,” or “into the midst of the children of Israel, the son of an Israeli woman” etc. similar to the expression: and he went out into the midst of the city, meaning that he [Mordecai] went out from his house or from where he was abiding into the city. Similarly, this [son of an Israelite woman] went out from his tent or from his place, and came into the midst of the people, and they strove there. The meaning of the word bamachaneh [“in the camp” — and the son of the Israelite woman and a man of Israel strove together ‘in the camp’], is that the quarrel took place in the camp and many people heard it, and [when they heard the son of the Israelite woman blaspheming the Name], they took hold of him and they brought him unto Moses into [his] tent. And the reason why Scripture mentions this episode here, is as the words of the Sage 23) and mentioned in Rashi. who says: “He ‘came forth’ from the section above [i.e., he began his argument by speaking contemptuously of a law mentioned in the above section], for he sinned with his lips concerning the fire-offerings of the Eternal, and an Israelite man rebuked him, whereupon they strove and he became angered and then blasphemed “himself.”
The intention of the expression the son of an Israelite woman and a man of Israel, is to teach that if a non-Jew has sexual relations with a Jewish woman, the child is not deemed Jewish. And although we have rendered the final decision in the Gemara that if a non-Jew has sexual relations with a Jewish woman whether she is single or married, the child is a fully-qualified Jew, yet they have said, “the child is ‘rejected,’” meaning that it is disqualified for the priesthood; and certainly it is not considered a fully-qualified Israelite by name as far as genealogy is concerned, with respect to the standards [i.e., as to where he was to take his place under one of the four main standards that were set up], and inheriting of the Land, for it is written of them, according to the names of the tribes of their fathers., 26:55 (with respect to inheritance). With regard to the …

והוא בן איש מצרי, this is why he had the effrontery to curse the tetragram; none of the Israelites would have been so deficient in reverence.

והוא בן איש מצרי, “whereas he was the son of an Egyptian man.” It was the fact that he had Egyptian blood in his veins that was responsible for his cursing G–d. We know that Pharaoh did the same when Moses first met him, and he denied the existence of Hashem. (Exodus, 5,2) by ridiculing the idea that he, Pharaoh, should have to accept directives emanating from Hashem.

וינצו במחנה, “they quarreled inside the camp.” This son of an Egyptian father was belittled by a normal Israelite who told him that it had been Moses who had killed his father. When this man asked the Israelite how Moses had killed his father, he was told that Moses had killed him by cursing him using the ineffable name of the Lord. Having heard this, this half Egyptian immediately retaliated by cursing this Israelite using the name of G–d to do so.