It's hard to come up with a reason for somebody who is a governor moving their child to another school just down the road that doesn't reflect badly on the school. But there might still be one.
@Schooldinners1 Was the parent a very new governor? (Might well have been, if their child was only in Reception?)
Maybe it's all about them: perhaps they fell out with the HT without especially good cause and decided to throw their toys out of the pram and flounce because of that.
Or maybe it has something to do with their child personally; I was a governor for many years and would still recommend that school for the vast majority of children DESPITE them utterly failing my own child - resulting in serious anxiety and school-based trauma. I could and still can see both sides of that particular situation. If your own child is really struggling then it's a hard line to walk as a governor and I wouldn't blame someone for throwing in the towel if it was still very early days. Much easier to start afresh and just be a parent, not a parent governor.
Or maybe they uncovered, with all the extra information they were privy to as a governor that isn't available to parents, a serious issue that made them no longer feel it was a safe/suitable place for their own child to be educated. You'd hope they would take follow-up action on this, if so, but people often do what's easy rather than what's right.
Ultimately you won't know unless you actually ask the former parent/governor. But even then you'll only get their side of the story. And school won't talk to you about it, so you'll never get their side of the story.