וְאֶלְעָזָ֨ר בֶּֽן־אַהֲרֹ֜ן לָקַֽח־ל֨וֹ מִבְּנ֤וֹת פּֽוּטִיאֵל֙ ל֣וֹ לְאִשָּׁ֔ה וַתֵּ֥לֶד ל֖וֹ אֶת־פִּֽינְחָ֑ס אֵ֗לֶּה רָאשֵׁ֛י אֲב֥וֹת הַלְוִיִּ֖ם לְמִשְׁפְּחֹתָֽם׃
A Elazar, syn Ahrona, pojął sobie jednę z córek Putiela za żonę, i urodziła mu Pinchasa. Oto głowy rodów Lewickich, podług rodzin ich.
Rabbeinu Bahya
Another approach: There is a mystical element here when the Torah writes of the four sons of Aaron, two of whom had already died and who certainly were not part of this census anymore. The Torah had described Nadav and Avihu as having died “before the Lord” (verse 4). It is reasonable then to understand the words “these are the sons of Aaron” as referring only to Nadav and Avihu whose death is being repeated in verse 4. Seeing that all four of Aaron’s sons had been anointed with sacred oil, we would have to understand the word לכהן at the end of verse 3, normally translated as: “to function as priest,” as meaning לכוהן, “to be priests,” a reference to someone who would function as priest after his father had died, i.e. Pinchas son of Eleazar. This would also account for Exodus 6,25: “she bore for him Pinchas the heads of the Levites according to their families.” This is also why again at the beginning of Parshat Pinchas (Numbers 26,60-61) the birth and death of Nadav and Avihu is once again mentioned. This is also why in Numbers 25,11 the Torah troubled itself to again trace Pinchas’ genealogy back to his grandfather Aaron. Seeing that the entire Torah is full of hints with profound meanings the Torah here saw fit to refer to these sons of Aaron three times. The first mention covers the intellectual relationship of these sons to their uncle Moses. The second time their existence is mentioned is a reference to their physical existence. The third time they are mentioned was to reveal to us something about the nature of G’d’s system of Justice, how instead of indulging the great it does the reverse and measures each one of their actions minutely. Seeing that two of these insights into G’d’s mind were revealed at the same time, the Torah used the conjunctive letter ו in introducing chapter three with the word ואלה. Seeing that the sons of Aaron had to be mentioned, the Torah also had to repeat what happened to them and why.
Rashi
אתם ואת פינחס [MOSES SENT THEM … TO THE WAR], THEM AND PHINEAS — The repetition of the word אתם, “them”, in association with Phineas’ name tells us that Phineas was regarded as equal to all of them together. — But why did Phineas go and Eleazar did not go? The Holy One, blessed be He, said, “He who made a beginning with this meritorious work, in that he slew Kozbi the daughter of Zur (who was a Midianitess), let him complete it”. — Another explanation why Phineas and not Eleazar went is that he went to take vengeance for Joseph, his mother’s ancestor, as it is said, (Genesis 37:36) “And the Midianites sold him [unto Egypt]”. And from where do we know that Phineas’ mother was of the family of Joseph? Because it is said, (Exodus 6:25) that she was “one of the daughters of Putiel” (see Rashi on that verse) — which is explained to mean that she was of the seed of Jethro who used to fatten (פטם) calves for idolatrous worship, and of the seed of Joseph who overcame (שפטפט, who talked or argued with) his passions (cf. Sifrei Bamidbar 157:4; Sotah 43a). — Another explanation: Phineas went because he was the high priest anointed for war purposes (cf. Deuteronomy 20:2 and Rashi thereon) (Sotah 43a).
Rashi
פינחס בן אלעזר בן אהרן הכהן PHINEAS THE SON OF ELEAZAR THE SON OF AARON THE PRIEST — Because the tribes spoke disparagingly of him, saying, “Have you seen this grandson of Puti the father of whose mother used to fatten (פטם) calves for idolatrous sacrifices (see Exodus 6:25 that Eleazar his father had married a daughter of Putiel who is identified with Jethro; see Rashi on that verse and Exodus 18:1), and he has dared to slay a prince of one of Israel’s tribes!”, therefore Scripture comes and connects his genealogy with Aaron (Sanhedrin 82b).