His phrasing, "I wish my son alive again" is particularly important, because it affects how the monkey's paw will grant the wish. Because the paw is cursed, it is designed to grant your wishes, but not in the manner you intended. Thus, by wishing his son "alive again," Mr. White seals his fate. Herbert does indeed come back alive, but as some sort of zombie or monster. Mr. White recognizes this, and to save his wife, he uses his last wish to return Herbert to the grave.
Had he worded his wish differently, the results may have been different as well. However, since the paw was cursed, nothing good could come of its use.
Mr. White, at his wife's frenzied insistence, stated "I wish my son alive again," as his second wish. This followed his first wish that went terribly wrong, when he asked for 200 pounds. The Whites received their wish in the form of a settlement from the firm Maw and Meggins, compensation for the death of their son in an accident in which he was caught in the machinery.