This statement captures the assumption: "I object to the idea that a male can decide he’s a female and that’s enough to make him one."
This is the same argument of "choosing" or free will that has been largely put to rest in regards to homosexuality. It's just resurfacing in the transgendered debate.
Not being an expert, I have to admit to guessing there is a transgendered range from radical transition as in surgery to demonstrating behaviors of the gender one feels comfortable in. Regardless, I can't imagine why anyone would want to suffer the social stigma, let alone surgical trauma to be able to enter a woman's bathroom. But the crux is that this is seen as a choice, not deterministic. As such, it goes to the root of the biblical "bad seed" who intentionally commits a sin.
But why not worry about lesbians in bathrooms? Just because their biology is the same, they still find themselves interested in women. Why are they not a threat, but a transgender person is?