Our Gemara on Amud Aleph states that should a person attempt to marry someone who is prohibited by a lo saase (chayevei lavin - prohibition without additional consequence of kares or death penalty), the marriage bond is valid. This is in comparison to a prohibited relationship that incurs kares or death, wherein the marriage would not be valid. The Gemara uses a scriptural deduction from the first born inheritance rules to prove that marriage to Chayevei Lavin is valid:
Devarim (21:15-16)
כִּֽי־תִהְיֶ֨יןָ לְאִ֜ישׁ שְׁתֵּ֣י נָשִׁ֗ים הָאַחַ֤ת אֲהוּבָה֙ וְהָאַחַ֣ת שְׂנוּאָ֔ה וְיָֽלְדוּ־ל֣וֹ בָנִ֔ים הָאֲהוּבָ֖ה וְהַשְּׂנוּאָ֑ה וְהָיָ֛ה הַבֵּ֥ן הַבְּכֹ֖ר לַשְּׂנִיאָֽה
If a man has two wives, one loved and the other unloved, and both the loved and the unloved have borne him sons, but the first-born is the son of the unloved one
וְהָיָ֗ה בְּיוֹם֙ הַנְחִיל֣וֹ אֶת־בָּנָ֔יו אֵ֥ת אֲשֶׁר־יִהְיֶ֖ה ל֑וֹ לֹ֣א יוּכַ֗ל לְבַכֵּר֙ אֶת־בֶּן־הָ֣אֲהוּבָ֔ה עַל־פְּנֵ֥י בֶן־הַשְּׂנוּאָ֖ה הַבְּכֹֽר
when he wills his property to his sons, he may not treat as first-born the son of the loved one in disregard of the son of the unloved one who is older.
כִּי֩ אֶת־הַבְּכֹ֨ר בֶּן־הַשְּׂנוּאָ֜ה יַכִּ֗יר לָ֤תֶת לוֹ֙ פִּ֣י שְׁנַ֔יִם בְּכֹ֥ל אֲשֶׁר־יִמָּצֵ֖א ל֑וֹ כִּי־הוּא֙ רֵאשִׁ֣ית אֹנ֔וֹ ל֖וֹ מִשְׁפַּ֥ט הַבְּכֹרָֽה
Instead, he must accept the first-born, the son of the unloved one, and allot to him a double portion of all he possesses; since he is the first fruit of his vigor, the birthright is his due.
The Gemara rhetorically asks, “Is there one who is loved by the Omnipresent and one who is hated by the Omnipresent?” Meaning to say, do we need a verse to tell us that it is improper to shift the inheritance away from a first born son that is hated? Honoring the first born is a Torah value and why should it be affected by personal likes and dislikes? Therefore the Gemara infers that the child is hated by virtue of the marriage, that is, he is a product or marriage to a forbidden woman which is indeed hateful in the eyes of God. From here we see that marriage to Chayevei Lavin is valid, since it is hated marriage, but nonetheless called a marriage by the Torah.
Rashi in Kiddushin 68a and Tosafos here (“Vechiy”) understand the Gemara’s rhetorical question as we explained above, that personal likes or dislikes should have no impact on the firstborn which is Torah value.
The Torah Temimah suggests a different peshat, based on a similar Gemara (Pesachim 113b):
“If you see the donkey of he who hates you lying under its load” (Exodus 23:5). The Gemara clarifies this verse: What is the meaning of he who hates you mentioned in the verse? Are we permitted to hate a fellow Jew? But isn’t it written: “You shall not hate your brother in your heart” (Leviticus 19:17), which clearly prohibits the hatred of another Jew? We must say it is referring to a person whom you have seen sin and know is a sinner, He is therefore permitted to hate him for his evil behavior. Yet, even so, we are commanded to assist him with his load!
Torah Temimah suggests that the Gemara’s rhetorical question here also is how can the Torah blithely refer to a hating a wife, which implies tacit approval to hating another Jew. The Gemara then gives a similar answer, that the hatred is stemming from the sin.
Torah Temimah’s peshat corresponds so well with the sentiment of the Gemara in Pesachim that it is difficult to comprehend why Rashi and Tosafos did not interpret our Gemara his way?
I believe the answer is that hate in marriage is not the same as hate in other relationships. When the Torah uses the word hate in marriage, it only means relative to the love of the other rival wife, or relative so some other concern, but not actual seething enmity. The proof text for this is how Yaakov’s feelings about Leah are described (Bereishis 29:31):
וַיַּ֤רְא ה׳ כִּֽי־שְׂנוּאָ֣ה לֵאָ֔ה וַיִּפְתַּ֖ח אֶת־רַחְמָ֑הּ וְרָחֵ֖ל עֲקָרָֽה
Hashem saw that Leah was “hated”, so Hashem opened her womb to allow her to become pregnant.
The obvious question is shall we believe Yaakov hated her? And if so, would the Torah allow for such insensitive Behavior without comment? In addition, an earlier verse (29:30) says that Yaakov loved Rachel MORE than Leah, but nonetheless Leah was loved, not hated. The commentaries offer different approaches:
Ohr Hachaim suggests ONLY Hashem saw, because Yaakov hid his feelings and behaved kindly toward her. Still Leah FELT hated. (You know, it’s very difficult to hide your true feelings from your wife, a lesson in and of itself.)
Bechor Shor says, Leah FELT hated relative to the fact that Yaakov loved Rachel more. Another lesson in and of itself, that not being loved enough is as excruciating as hate.
Interestingly, Chasam Sofer suggests that Hashem was concerned that Yaakov might come to hate her, so He gave her a head start in terms of establishing her credentials as a matriarch.
In any case, this approach explains why Rashi and Tosafos did not learn the Gemara like the Torah Temimah, as the word hate itself can be scripturally used in a relative sense to a co-wife, without meaning enmity. Therefore the question of the Gemara is referring to the process of firstborn rights and how love or hate could possibly impact upon it.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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