I find it ironic that you make your argument this way, when the statement that it is not theft is generally exactly intended to highlight the moral issue.

To me and a lot of others, illegal copying is far more morally defensible than theft. If someone tries to call a person that pirate a thief, my immediate reaction is that the claim is not only flat out false, but offensive.

Copyright protection is an artificial government monopoly on an activity that does not affect your property rights, and as such it is perfectly defensible for someone to consider it moral to violate copyright. I do consider some forms of copyright violations morally wrong, such as selling copies, but I do consider a lot of piracy morally acceptable (despite the fact I don't engage in piracy, though I did some 20-25 years ago)

Theft is materially different because it deprives the owner of continued use of that which was stolen.