Well, that’s clearly false. There are many cases where something is bad for an individual yet neutral or beneficial to the state. An obvious example is that of a criminal or traitor - his punishment is bad for that individual, but is a net benefit, or at least no penalty, to the state.

I said wrong, as in morally wrong, not bad.

rights do not exist except in the context of what we collectively agree to bestow upon others and ourselves.

False, unless of course you are going to argue that people don’t have the right to life unless the collective agrees.

This claim fails every reasonable moral test almost instantly.

Why does every right imply a responsibility?

Because exercising those rights require you understand how they impact the equal rights of others.

If I have the right to own property, do I then have a responsibility to own property?

No, rights imply responsibility, remember. The responsibility is that ownership of property does not violate the equal rights of others in some way.

If I have a right to self-determination, do I have a responsibility to make every decision for myself? Why do rights imply responsibilities?

You have a right to self determination, and if you make decisions for yourself you have a responsibility that those decision do not violate the rights of others. You seem to be going a little on the absurd side here.

Why do property rights exist? If you say you own something, yet I take it away from you, why have your rights been violated? After all, I own that thing now. What, other than your desire, grants you a right to that property?

Actually quite simple property is gained either through mutual trade or exchange or by mixing your labor with raw goods, land or materials not owned by someone else.

So basically it boils down to you don’t believe in natural rights or liberty, but rather the power of the state? What do you believe to be the foundation of rights?