Wang Lung's father is of a generation who traditionally relied on the earth to provide for its needs. He also belongs to a generation who worked hard in its youth and prime to provide for a family and raise sons who would one day be strong and successful enough to take care of the elderly when they are no longer strong enough to take care of themselves. It was a traditional homage and respect for the young to revere the old and take care of them as they aged.
As a result, Wang Lung's father does not beg.
I have plowed and I have sown seed and I have reaped harvest and thus I have filled my rice bowl. And I have beyond this begotten a son and son's sons. (Chapter 11)
First, he means that it is beneath his dignity to beg. Further, he believes that he has done everything he could have done (with integrity) and now he deserves to be taken care of in his age. This old man believes to his core that it is his son's and his grandsons' responsibility to provide for his own needs.