"That's because you don't have children"
You haven't actually proven me wrong in any sense, you've just presented an alternate reality where I would be wrong, which you've framed as an argument against what I initially said. This assumes I am wrong, otherwise you would have agreed with me because there's no logic in presenting a rebuttal to an argument based on nonexistent data (hence the "logical fallacy" part).
The phrase "If you had children..." is always either a case of Bulverism or simple platitude; irrelevant either way. And given the number of times I've heard it, we should probably all be glad I don't have children ;)
That's why I don't really feel that my statement fits the definition of Bulverism. I had no intention of proving you wrong, nor did I assume you were wrong. After all, who knows how you felt about the subject better than you? Because of that, there was really no point in agreeing with you, unless I thought you were lying, and since I don't know you, I'm giving you the benefit of the doubt. =)
Doing further research, I found the following statement on Bulverism: "The Bulverist’s thought is that if a person’s convictions can be fully explained as a result of non-rational factors then we need not bother about those convictions." Now I consider both the childless and child-laden conclusions to be very rational, though you're probably right in that it's a platitude, I don't hang out with child-laden people often enough. =)
Based on the definition on Wikipedia, I'm not sure my statement qualifies as Bulverism. The definition says that I assume your statement is wrong. What I did was state that if a certain condition exists, you might have a different opinion, which is to say that I assume your current statement is correct. If I misunderstood the meaning of Bulverism, please let me know.