There are many ways in which interracial marriage is harmful to society. For one thing, it’s often used to “marry up” as Jump4Joy said. This results in it being harder for certain groups (in the US, Asian men and black women) to find spouses, and in the long run it creates societies highly stratified along (de facto) color lines, which persist for centuries or even millennia after the original race mixing took place (e.g. Latin America, India). Moreover, children of interracial unions are much more likely to suffer from identity issues. And of course, the ultimate harm that comes from mass mixing is that it leads eventually to the extinction of the groups involved, since they cease to exist as separate groups.