On the other hand, if you're having an affair with someone that you have a good excuse to talk to all of the time (family friend, co-worker, etc), the content matters.
Also, that "OMG you were talking to a pedo!" threat doesn't mean much of the conversations were innocuous. To make that threat, they would need a good confidence that you couldn't (for whatever reason[1]) just turn over chat logs proving that nothing was amiss.
[1] E.g. The chat reveals something you want to keep hidden, even if it doesn't relate to the fact that the person is a paedophile, or maybe the logs just don't exist, etc.
Also, that "OMG you were talking to a pedo!" threat doesn't mean much of the conversations were innocuous. To make that threat, they would need a good confidence that you couldn't (for whatever reason[1]) just turn over chat logs proving that nothing was amiss.
[1] E.g. The chat reveals something you want to keep hidden, even if it doesn't relate to the fact that the person is a paedophile, or maybe the logs just don't exist, etc.