In my industry there is a joke that has a great stonking grain of truth with it that you are not a real manager until you've had a complaint made against you.
OP I think sometimes it's because we have to make constant judgement calls and frankly you'd be a magician if every single one was right , sometimes it's because people need to kick something and unfortunately we are the person to kick , some people are entirely convinced all managers are evil (goodness knows I've seen some posts on MN that reinforces my belief on this) and sometimes we deserve it.
Try not to take it to heart but consider it, if you are genuinely assured you were not unfair or unreasonable remember that it's the complainant stuff.
The other thing is half the time people dont see what the manager does for their staff. I train managers now , and I always tell this story. I had a member of staff that royally royally screwed up in front of the commissioner. However I knew fully that his wife had just left him and despite making him take time off I couldn't stop him returning too early , he made the mistake in this time period.
I spoke to the director and insisted I took the hit , because he would pull it round and it was the right thing to do. My God, I sat in front of two commissioners and they absolutely tore strips off me (I didn't lie I just insisted that as the senior manager it was ultimately my neck and wouldn't give them the name) , for two hours I got it. I took it all and didn't tell him (the issue had been resolved and he had never made it before or after )
A month later he made a complaint about me because i told him to get off of his personal phone kn front of a client.
Apparently he was particularly nasty about me, my director who knew the whole story , pulled him into her office and told him everything, what I had done, the fact that cameras backed me that he had been on his phone, other staff had backed me that I had been polite and professional and she reminded him I had had his back.
His response... "well I felt she was being picky and I know im right"
People are asses and their boss is an easy shit. I do think it's part of management to let it roll off of you.