it's mine so I can do what I like with it ....
                                                             ... if it doesn't hurt anyone else.

I've often met this line, and it has usually been going somewhere I don't like.  So here is what I think is wrong with it.

The first problem is with "hurt" (or "harm" or "violate the rights of").  Consider some examples.  A has undisputed ownership to an oasis as B comes crawling across the desert up to the fence.  A doesn't let B in for a drink and B dies of thirst.  Did A harm B?  He hadn't squashed him with a rock, but he has failed to give him help.  Is failing to give help a matter of harming?  That's the distinction between acts and omissions, as moral theorists say, and they all agree it is a hard distinction to sustain.  It is sensitive among other things to what language one is using, and what active verbs are available.  But surely that is irrelevant.  If we are speaking a language with no word for "shoot" but an active word for refraining from shooting ("sparing ones aim towards" might be a translation), then it isn't much defence if A shoots B that he only refrained from giving B the assistance of refraining his shot.  Or I notice that there is a misleading sign that gives the impression that a public path goes across my land.  So I dig a deep pit and fill it with alligators, then watch and giggle while hikers fall into it.  Have I caused their deaths?  I didn't push them. but I didn't warn them either, or help them out.  One definition of cause is that one event causes another when if the first hadn't occurred then the second would not have.  Add to this that to harm someone is to cause injury to them.  Then the pit digger has harmed the hikers.  But on this definition of cause there is no act/omission distinction: if you are harmed because I refrain from helping you, then my refraining causes your harm.  Want a different definition of cause?  You're welcome to look for one.

The second problem is with "anyone".  A particular person?  But many things you can do with your property affect people who do not yet exist, or whose identity is undetermined. Suppose you own the only supply of a rare earth that will allow technology that will save lives, and you vaporize it.  Besides the present people who you have failed to help, there are the great-great-grandchildren who will die, though there is no present fact about who they are and how many they are.  Are you implicated in their deaths? A matter of how we twist the terms.  But if you had acted differently they would not have died.  

Problems about cause and problems about specificity ('harm" and "anyone") combine when the uncooperative behaviour changes the probability of bad things happening to people.  Suppose that I and my pals joyfully expose ourselves, on our land, to a mutant virus that is sweeping the country, then go and have a drink in town.  We make it more likely that babies and old people will die of the virus.  Have we killed them?  Unclear, since the virus was circulating anyway and we didn't target anyone in particular.  But more people are likely to die as a result of our acts.

The third problem is with "can".  If it means "legally permissible" then the claim is generally true in many legal systems: I have legal permission to dispose of my property as I wish.  But with important exceptions: I can't legally burn all my money before paying taxes, and in many jurisdictions there are restrictions on how much I can leave to whom.  But of course many things are legally permissible that are wrong.  "Can" might mean "I have a right to do it".  Then the argument can get long, because there is not much agreement about what rights people have. (The core of the consensus takes "A has a right to do E" to mean "it's not permissible to prevent A doing E".) But on the core of "right" that we all agree about, it can be wrong to do something you have a right to do. If I have more money than I know what to do with and you are my handicapped grandchild and instead of leaving anything to you I have it all thrown in the sea then I am probably acting within my rights, but this doesn't affect whether what I have done is right.  Or I discover a mortifyingly embarrassing fact about you and I describe it on a billboard -- on my property -- and you are so humiliated that you kill yourself.  Then I am within my free speech rights, but I have done wrong.   So we can criticise people who are doing things they have a right to do, and adopt various means to persuade them to act otherwise.

This is the issue when someone points to their having a legal right to do something, as if that refutes criticism of them for it. Often the right means that others cannot physically prevent them from doing it (though they can change the law). But they can say loudly that is is wrong, and try to persuade the wrong-doer to act otherwise.  Then the rights-worshipper is often annoyed and confused.  "But you can't interfere, I have a right to it."  To which the reply is "So we can't physically stop you, but there are many other things we can and should do."

The fourth problem is with "mine".  Concepts of property - what you can own and what owning it entails - vary from culture to culture.  We don't think one can own air. In French law one owns one's land down to the core of the earth, but that is not so in the law of other countries.  Questions of intellectual property rights are very contested.  In some countries there can be a right to cross someone else's land, but not in others.  It's a social invention.  Probably a good one, but the devil is in the details.  If you own some woodland, you don't own the air above it.  Do you own the water below it, or the widlife within it?  That is a matter of how we make our law. 

What to conclude?  Crudely, that it is not true that if I own something and I use it to act in a way that does not directly cause harm to another person, then I have not done anything wrong.  Right and wrong are always vague and contested, but it is hard to see how the claim could be true on even the bare intersection of the moralities that sane and well-meaning people accept.

 An afterthought:  There's a connection between the issues about rights and questions of tolerance and relativity.  People have different views about what is right, and most of us agree that it is good to tolerate, even indulge, one another's crazy opinions about morality.  So we say that you have a right to your own opinions here.  This means that if I disagree with you I cannot force you to stop thinking or expressing yourself the way you want.  But it doesn't mean I cannot try to persuade you that you are wrong.  Sometimes I have a duty to, in fact.