From the persepctive of the Governing Body, there is always more than one story. From yours, it depends what you want - a mistake remedied, a better relationship because misunderstandings are corrected, or something else. Ask yourself if it's within the gift of the Chair. The school has to go on, how critical is your incident to its immediate and subsequent effective functioning?
Things are not perfect, we don't always have the whole picture, it may not be entirely possible to reconcile different viewpoints and individuals. You will almost always not get everything you want, unless it is something basic (e.g. the gross misconduct type events). There will always be damage, to you and others, although at best this is temporary.
So it is probably about being clear as to what you want (immediately and after) and whether it's worth pursuing, and whether you're prepared to change your position if given new facts, and what you would do if it goes against you. Most parents go for a happy outcome for their child, and schools competent in pastoral care will work on that. Most Governing Bodies go for a happy outcome for the school, which will include your child because that's what good schools are about. Bear in mind also that this varies with the calibre of the school/ Governing Body.