A very mildly flirty and very brief conversation with a member of the opposite sex, is not infidelity, it's not even particularly inappropriate. It's meaningless light hearted banter.
Agreed, and making it private can only lead to suspicion that it is something more serious than it is.
I'm obviously in the minority on this, but to my mind 'privacy' means that there are secrets, and mistrust as to how a partner may view them if he/she found out.
From the very start my DP and I have been entirely open about everything in our personal lives, including previous relationships. It means we can have absolute trust in each other.
If I wanted to keep secrets from DP I would have to question myself why I couldn't trust him to know them. And I know he feels the same because he has said so.
The Relationships board is full of people suspicious because their partner has hidden emails. texts or voicemails, and wondering what this may mean.
The only things I keep from DP are plans to buy him presents or arrange surprises for him.
But clearly others here feel differently.