Marriage itself isn't always intentional, somtimes it is a socially enforced consequence of copulation that results in procreation, at least in western societies.
While it may not actually be the actual result, the cultural "norm" is that men and women come together to form a unit. Together they have a child, or multiple children, and their offspring go on to do the same. Even if it doesn;t work out that way, the idea still remains the same.
Even if a human is divorced, the "social norm" is that the family "unit" is still in a way tied together, (through things like alimony, and child support.)
Even before the idea of divorce, you can see how a child outide of a married couple was considered "outside the norm" the term "bastard becoming an insult and such..."
And you can even see it in the above statement. If they have a child out of wedlock, society almost pressures them to get married... Because the "societal norm" is that two parents come together to raise a child.
To a human, if you say "I got a divorce." a valid responce could be: "I'm sorry things didn;t work out between the two of you."
Dragonborn society would be completely different.
Two Dragonborn come together out of the need to procreate. Once they've done that, they move on. No concept of a continued family unit (divorced or not.)
One parent maintains the child, the other moves on to the next.