Of course it's not the same to duplicate information as it is to remove a physical item, but both are based on an artificial legal concept of property.
The natural state of things is indeed that I can copy any information coming my way, and copyright artificially restricts my right to do so in the eyes of the law.
Then again, the natural state of things is also that if you have a physical item and I want it, then if I am bigger than you/have a bigger gun than you/have more friends than you, then that item is now my possession and not yours, and theft-related statutes artificially restrict my right to take it in the eyes of the law.
In the end, copyright, like physical property, is an economic tool. Society gives it the force of law to make sure that people don't game the system unfairly. It makes no sense to debate that law, in either letter or spirit, without considering the economic implications of breaking it. Those implications are not zero just because information that already exists can be reproduced with near zero marginal cost and time overhead using modern technology.
In other words, many philosophers do draw a morally relevant distinction between these categories of rights.
Also, I'm sure you can see how those who are copying/stealing/whatever you want to call it might wish to call it copying instead of stealing, as that implies a lesser moral judgment (deservedly imo).