In a yes/no question, a student gives the right answer and an unnecessary but wrong explanation. How to grade?
You asked for a yes/no answer (which, as you've discovered, has its disadvantages) and got one plus some other stuff. You should grade the yes/no answer and ignore the other stuff. If you like, you could add a note like "You got lucky! This is actually because..."
The whole point of yes/no or MC questions is that you grade only the answer, and assume that type-1 and type-2 errors cancel out or are normalized out. That paradigm doesn't work if you don't uniformly ignore everything other than the answer.
More concretely: other students likely got this question right using the same incorrect reasoning, but didn't write their reasoning down. There is no way to identify these students; so, you need to make sure they get the same score as this student.
I think that if you would allow full marks for just yes/no without an explanation at all, then you should allow it here. Otherwise the question is flawed and can't be properly and fairly graded. But a note to the student would be good, also.
To be more precise, if it is possible to answer a question with inconsistent parts it isn't a valid question for examination. It should be clear and clean.
But your job is to educate, not to grade. Give the marks and write the note. And think harder about the questions you ask and how they are presented.
If the explanation is required, it is a different situation. In that case, and if you weight the explanation heavily for other students, then probably 0 marks is better than any other alternative.
This is a discretionary matter, and different lecturers will treat it differently, depending on their own educational preferences. However, I disagree strongly with some other commentators on this thread. In my view, there is nothing unfair in marking a student down for unsolicited and incorrect information. Indeed, I would say that this is generally a good practice, since it ensures that the student is held responsible for the correctness of their assertions, even in cases where they offer unsolicited information. This implicitly gives the student some broader training in the importance of ensuring that they give correct information even when they choose to advance information that is unsolicited --- something that is a broader life-skill of importance.
In my personal practice, if a student gives me more information than was requested, and that additional information is wrong, this incurs a marking penalty just as if that information was part of the question. I warn my students in advance that this is my practice, but it is a justifiable practice even without giving a warning. In this particular case, if I were marking the question, I would not give the student full marks.
What kind of graduates do we want? We are training students to become professionals in difficult fields. So, in considering this issue, I think it is important to consider the implicit lessons we give students by what we penalise and what we don't. Imagine that this student graduates and practices in your field. Would it be okay if this practitioner gives unsolicited information to people on the subject area, and that information is wrong? Would you be comfortable working with a colleague who gives information to you or others that is sloppy and incorrect, but then he faces no penalty just because that information was not requested by others? Is that the lesson you would like to impart to your students? Is that what you want to teach them about the world?