I think it does. Because my assertion is that your argument proves too much, and these are some examples of "too much". If you don't agree that these cases also match your argument, then either you are being inconsistent, or the argument you've advanced is not actually your argument.

To put it another way, to those who say "all that should be required for a marriage is two people who love each other", I say: "Two? Why just two, you discriminatory bigot?"