This is not true as an absolute statement. If it were then libraries would be immoral.
There are a couple of things that you are missing:
One thing is that copyright is not a natural right. No one naturally has a right to restrict copying of some work they have created. Copyright is a limited right created by law. If copyright were a natural right, then it would not be of limited duration. After all, it’s not ok to steal someone’s jewelry just because they have owned it for a long time years already, but it is ok for anyone to reproduce and sell books from anytime before the early 20th century, because the copyright on those works has expired.
Another is that copyright is not theft. Theft is when you take possession of someone else’s property, thus depriving the rightful owner of the use and enjoyment of that property. A copyright infringer does not deprive the copyright owner of the use and enjoyment of the copyrighted work. If copyright were theft, then it must always have been theft, and forbidden by the 7th commandment. If so, then all the monasteries of medieval Europe were continually breaking the 7th commandment as one of their primary occupations was to copy books (without securing licensing or paying a fee to do so).
Lastly, a simple look at the history of copyright shows clearly that the concept simply didn’t exist more than about 300 years ago. At the time of Shakespeare, for example, there was no copyright law and books were copied by printers all the time. One of the earliest seeds of copyright law was the efforts of the Church to control the printing of sacred texts, such as missals, and Bibles. But this was not done out of an abstract notion of copyright as we think of it today, but was rather a matter of preventing sloppy and error-prone editions of these important works being produced by unscrupulous printers out to make a quick profit.
Not at all, because to do so would be to break the law, which does not permit non-holders of copyright to publicly perform copyrighted works. Limited personal use, however, is often permitted by law. Recording television shows for later personal viewing, for example, is legal.