I feel that "copying is not theft" is a truth that needs to be clarified because a lot of discussion around copyright and piracy tends to conflate copying and theft, which makes it natural to skew towards the point of view that the unauthorized sharing of content and ideas is an objectively immoral act, and paint the issue of piracy in terms of right and wrong, as opposed to legal vs. illegal. Whereas in my point of view, copyright law is an artificial construct that we as a society have chosen to enact, in order to support a certain model for financially compensating those who make creative works. Other societies may choose differently; copyright law is not a reflection of natural, fundamental morality regarding the sharing of ideas and creative works.
In conclusion, when I personally say "copying is not theft", I'm simply saying, let's not conflate the issues, so we can have a more nuanced discussion. I'm not advocating piracy. And I would encourage others not to interpret "copying is not theft" that way.