Who you marry affects every single aspect of your life. It affects your community. It affects your children. It affects all future generations. The Jewish home is the single most important establishment in Jewish life. It outweighs any synagogue or temple, even the Holy Temple built by King Solomon. By marrying a non-Jew one thereby ends over 3,000 years of Jewish continuity, effectively cutting oneself and one's offspring off from what it means to be Jewish.
There have been many other arguments offered against intermarriage, below is a summary of some of the most famous.
1. Six million Jews were killed in the Holocaust, 12 million were left afterwards. Today there are only 13 million Jews in the world. Where are the rest that by natural increase should number close to 20 million? The answer is that the silent holocaust of assimilation has caused them to disappear as Jews.
2. Intermarriages are twice as likely to end in divorce as same-faith marriages (75% divorce rate!). Some reasons for this are the different identities of the spouses and the differences in culture and family. For example a Jew will naturally turn their head at the mention of "Israel" and "Jew." A gentile who converts in superficial and insincere conversion only for the sake of marriage does not create a new identity that is now Jewish.
3. One is granting a victory to anti-Semites who seek to destroy the Jewish people. Think of what has been sacrificed in the past by our own ancestors to keep their Judaism. And think of the heritage that is being sacrificed for the sake of personal reasons.
Ultimately, however, all Jews must have a sense of pride in their own identity. We cannot define ourselves by foreign ideologies, nationalities or religions. As Jews, we have a unique identity that is connected to our purpose in the world. We were chosen to propagate the ethical monotheism of Judaism.
Intermarriage is a betrayal of this task and a threat to Jewish continuity.
