(דברים ז) ג וְלֹא תִתְחַתֵּן בָּם בִתְךָ לֹא־תִתֵּן לִבְנוֹ וּבִתוֹ לֹא־תִקַח לִבְנֶךָ:
ד כִי־יָּסִיר אֶת־בִנְךָ מֵּאַחֲרַי וְעָּבְדוּ אֱלֹהִים אֲחֵּרִ ים וְחָּרָּה אַף־יְהוָֹּה בָּכֶם וְהִשְמִידְ ךָ מַהֵּר:
Devarim 7: (3) You should not intermarry with them: You should not give your daughter to his son, and you should not take his daughter for your son.
(4) For he will turn your son away from after Me and they will worship the gods of others etc.
Explanation #1 Rashi (Yevamos 17a)
Explains that the first verse (3) records two cases:
a) A Jewish woman (your daughter) marries a gentile’s man (his son)
b) A Jewish man (your son) marries a gentile woman (his daughter)
The “he” of verse 4 refers not to the gentile father-in-law; rather it refers to the gentile man that the daughter married. The verse warns that this gentile would influence the future child (grandchild) to follow his pagan gods. The Torah describes their child as “your son” to teach that despite the father’s status as a gentile, the son is a Jew.
However, this does not happen to the reverse case. The Torah uses the only the masculine form of the verb יסיר, and does not use the feminine form. The Torah makes this distinction in order to inform us that only when a Jewish woman marries a gentile’s man does the child remain a Jew. However, if a Jewish man marries a gentile woman the child is a gentile.
Explanation #2 (R. Tam Kiddushim 69b)
"Ki Yasir" refers to "do not take his (a Nochri's) daughter for your son." The Chosen (her father) will veer your son away from Me.
1. This veering means that the children are not attributed to your son, rather, to the Nochris. It is not called your son, rather, her son.
2. Shmuel and R. Yochanan did not explain anything about a Nochri who has Bi'ah with a Yisraelis;
i. Rather, Ravina infers that the son of your daughter from a Nochri is called your son, since it does not say "he will veer your daughter";
ii. Inference: There is no veering here, for the lineage [of her children] follows her.
Explanation #3 (R. Tam)
Shmuel and R. Yochanan infer from "Ki Yasir Es Bincha" that the Torah is concerned only for his (your son's) veering, lest he (his Nochri father-in-law) make him err;
1. The Torah is not concerned for your son's son veering, for since he comes from a Nochris, he is not called your son, rather, her son, since it does not say 'he will veer them' or ''he will veer your son and his seed away from Me.'
2. Ravina infers "we learn from this that the son of your daughter from a Nochri is called your son, for only regarding your son (marrying a Nochris), "Ki Yasir Es Bincha" excludes his seed, but regarding your daughter, even in his (the Nochri's) seed there is concern for veering.
Rabbeinu Bachyei writes that this is a prohibition even after they convert. The Torah was more stringent with these seven nations than with others because they were the most depraved, degenerate, and immoral nations upon the face of the world.
Torah Temimah cites a Talmud Yerushalmi that implies not only is the prohibition to actually marry, but also to assist in such a marriage, such as arranging the meeting, assisting in the marriage planning, etc.
