[jennyp]

If Utilitarianism be true it would be one's duty to try to increase the numbers of a community, even though one reduced the average total happiness of the members, so long as the total happiness in the community would be in the least increased. It seems perfectly plain to me that this kind of action, so far from being a duty, would quite certainly be wrong.

— C. D. BROAD, Five Types of Ethical Theory

I think the fallacy here is assuming that you can assign an amount of happiness or unhappiness to the state of never having been born in the first place. If a never-been-born child represents total unhappiness, then yes, producing him/her would increase the total H, no matter how unhappy their life was.

But you really can't assign a value, good or bad, to the life that never existed in the first place. So the equation is invalid.

[general_re]

Keep in mind that the passage presented may be describing a fallacy, rather than being a fallacy itself - 16 is a good example of this.

You may find the context of that passage interesting. The full text of Broad's Five Types of Ethical Theory is available here, and the passage in question is in this section.