The fat man makes the argument that the parents should not dwell too much on how they must give up their sons to the war effort.  He draws the picture of his own son who writes and conveys how happy he is to sacrifice his life for the glory of the nation.  This is what drives him in his own parental mindset and also helps to make very clear that parents must actively support and endorses the idea of children sacrificing their lives for a nation's war.  To quote Elie Wiesel, "When adults wage war, children die," and this is something that the fat man lauds and praises in his own son for support.  When the mother asks him about his own son's death, we see the crushing reality hit him, undermining his own rationalization.

Basically, the fat man is saying that parental love has to come second to one's duty to the country.

What he says is that parents do not have children for their own (the parents') sake.  They have children for the sake of the children.  When your sons get to a certain age, they want (among other things) to serve their country.

At that point, he says, you have to let them go.  You should be proud and happy that they want to serve the country.  If they die, you should be happy because they died doing what they wanted to do.  They died happy, so you should be happy too.

So he is saying that parental love is too selfish.  Parents need to think of the kids and the country, not themselves.