I think I see where you're coming from - "I respect your property rights, you respect my property rights" might sound equal but in practice what does a person with no property have to gain from such a rule? As the saying goes, "the law, in its majestic equality, forbids the rich as well as the poor to sleep under bridges, to beg in the streets, and to steal bread." My answer is twofold:
First, I consider respecting property rights a moral obligation. (You might find it strange that I think it's a more important moral obligation than helping people in need, but I do. I suppose that's why no one likes libertarians.) I wouldn't take from someone who had more than me unless I sincerely believed that he obtained it by unjustly exploiting me, not in the abstract sense of "the rich have rigged society in their favor" but rather in the concrete sense of "that guy stole my bike so I'm stealing it back." I imagine I would violate this principle if I was in desperate need (e.g. stealing a loaf of bread to feed my starving family) but I would feel pretty bad about it.
Second, I think everyone (including people who don't share my morality) is better off if we don't resort to violence. It's not just a personal matter of people stealing from me and my attempts to stop them via violence - individual acts of violence add up to create a violent society. I used to work with a guy from Brazil - he was trying to get residency in the USA because he felt like his upper-middle-class income was putting him in danger. In Brazil, people with money run the very real risk of being violently robbed or kidnapped. But people without money are also subject to more violence! Compare a slum in the USA with a Brazilian favela. So maybe if I'm rich and you're poor, you help yourself if you mug me but you're contributing to the creation of a society where no one except brutal organized criminals would be better off than they are in the USA right now.