Answers to Questions by Yair Davidiy (22 October 2017, 2 Heshvan, 5778)
Is Jewish belief, that someone is considered Jewish only if his mother is Jewish, based on fear that a non-Jewish mother can cheat on her husband and thus give birth to non-Jewish children which in turn won't have any Jewish blood?
One may suggest different rational explanations. There may be something to them or there may not. It makes no real difference. The fact is that this Law is based on the Hebrew text of the Bible. It follows grammatical and exegetical principles. God is the author of the BIBLE and HE decided that is the way it should be.
The Bible ( Translation by Yair Davidiy) says:
Deuteronomy 7: 3 Nor shall you make marriages with them. You shall not give your daughter to his son, nor take his daughter for your son.
4 For he will turn your son away from following Me, to serve other gods; so the anger of the LORD will be aroused against you and destroy you suddenly.
Going through it again: Deuteronomy 7:3 says: Do not give your daughter to his son. Nor take his daughter for your son.
Deuteronomy 7:4 says: He will turn your son away from me.
This means that he (the non-Israelite in 7:4) will turn your son (i.e. your grandson) away from following God.
The person in 7:4 who does the turning away is the non-Israelite husband of your daughter.
"Your son" is the offspring of your daughter.
Deuteronomy 7:4 says nothing about the offspring of your son with his daughter (mentioned in 7:3) since this is not your son nor your grandson.
Source: Talmud, Kiddushin 68 b, and legal explanations thereto.