"private reason" vs "personal reason"

From the Merriam-Webster Dictionary, private has quite a few meanings.

One of those meanings is this:

not related to one's official position

It sounds like that's the way you're taking his meaning. However, private can often (probably more often than the above) mean this:

intended for or restricted to the use of a particular person, group, or class

With this meaning, when I call something private, it means I don't want other people to know about it. If there's a death in the family and I don't want other people talking about it, I might call that a "private reason" for not attending an event.

So it sounds like you're using the first meaning, when the person in question might be intending the second meaning.