My father and I have a DNA match to a cousin but my son does not. How is this possible?
You inherit 50% of your DNA from your mom and 50% from your dad. On average that means you'll inherit 25% from each of your 4 grandparents. But the reality is that which DNA you get from each parent is completely random. You always get the same number and length of chromosomes, but you don't know which side (DNA being double stranded) you'll get.
So if your father's match with the cousin is A cM, then your match might be half of A, and your son's match might be 1/4 of A. But human beings are not averages. Maybe your match is small and your son didn't get any of the relevant segments (not ones long enough to count anyway).
If this is a very close cousin, then that's different. If your son is a full second cousin to this person then there should be a DNA match. If it's a more distant cousin, then often the match is 0.