It seems that younger people view marriage and children as two separate things. They may want to have children, but not want to be married. Many younger people, do not have the same hesitancy about getting pregnant outside of, or before, marriage. Lots of people get married and have kids. Some people get married and never have kids.
Some people get married, have kids, and then get divorced.
Getting married and having children are thus distinct, but tightly related. Perhaps a bigger cultural difference is the perception of age. It sounds like your boyfriend is interested in marrying you since he's talking about your future children. . But there's one thing I don't understand. I can understand the parents not wanting to get married for their own reasons, but to the child, the two of them are still indisputably his or her parents.