I recently had a dispute with an online retailer. The customer service representative really showed their colors in the emails they sent to me. I then wanted to show a social media forum this interaction so I posted our entire email conversation. The retailer threatened to sue me of k didn’t remove the remarks. Have I broken the law or am I being bullied?
An email is protected by copyright, and cannot be lawfully distributes without permission., However, it could be quoted from fairly freely under fair use (in the US) or fair dealing (in many other countries). Particularly since most emails have no commercial market, so their value cannot be impaired, a fair use defesne is likely to prevail in many cases. Moreover, most emails are not registered with teh copyright office, which would have to be done before a copyright suit could be filed.
As the answer by Iñaki Viggers correctly says, there is no duty of confidentialty unless you have agreed to one, which seems unlikely.
Thus, quoting key portions of such an email is almost surely legally valid, and no threats of legal action would be valid.
Have I broken the law or am I being bullied?
The retailer is just trying to intimidate you. It is lawful for you to publish the interactions unless (1) you agreed --even if tacitly-- to preserve confidentiality of the communications, or (2) your publications disclose third parties' information that ought to be redacted. At first glance neither condition seems to apply in your matter, but only you know the full details so as to assess whether that is the case.
In general, publishing the interactions helps preempting retailer's claims of defamation because you are giving the audience the opportunity to corroborate the basis of your denouncement of the retailer.