This entry really makes sense. One should, as the author contends, refrain from saying , "you cannot understand this because you don't have any children as I do." But it is not because one ends up, as the author states, in denying the other person with whom you are discussing by saying this, but because it gets the discussion nowhere.
This kind of remark is called "ad hominem" in critical thinking. It is a way of arguing intended to discredit the argument of people by denouncing them, not the argument itself. There are some kinds of ad hominem. The one about which the author of the entry thought is a circumstantial ad hominem. When you point out the situation in which people are placed that seems to lead them to hold their view, in order to make thier arguments less plausible, you have committed this fallacy. For what circumstances poeple find themselves in has nothing to do with the plausibility of their arguments.