(Pro 27:11 KJV) My son, be wise, and make my heart glad, that I may answer him that reproacheth me.
Do you have children? If not then they have never embarrassed you. Children have a way of saying less than wise things at less than right times. It happens. It is life. Usually it becomes something the family can joke about for years to come. That does not naturalize the possibility that your son doesn’t stand the test of time.
The test comes when they grow up. In today’s world that means that they will be out of step with the common culture. People may think you have reason to be embarrassed. People may think you are disappointed. If your son is walking the high road then it is the reproach that will not hold water.
So? If they are your children, raise them right. If they are not, be the best influence you can be. After that it is up to them.