They have a right because it's legal, is the point. This kind of argumentation is used, oftentimes, to substantiate abortion and to condemn attacks and attempts to restrict abortion. After all, this is a legal procedure. Morality is reduced to law. That's why the appeal to the fact that it is legal is considered adequate to silence the opposition.
People toss around rights language all the time.
People are plucking rights out of the sky like they grow on celestial trees, but when you ask the question, what is a right, people are hard-pressed to give you an answer. I understand sometimes people can't put into words what they know to be true, but I don't think that is the case here. I'll tell you what a right is. A right is a just claim to something. In other words, it is appropriate that they make the particular claim that they do.