Let me clarify that I understand how the asymmetric key signing process works. I am looking from a legal standpoint--how can you assign ownership of a BTC address to a person?

When I obtain a debit card, I have exclusive ownership over the use of the debit card address and the funds of that address because the bank (a centralized authority where the money is held) agrees that I (a person) own them. With BTC though, people randomly generate a private key to use and the person's identity is not attributed to that address in any explicit manner.
How can there be ownership in a system where there is anonymity? For instance, if no bank accounts had names attributed to them and people simply made transactions based on whether or not they had a pass-phrase or key to a certain account then how can someone claim that another person, for example, steals from them?

This question came to mind when thinking about people generating private keys based on phrases like brainwallet.org does. If someone generates a private key with a phrase that happens to already be in use (and has a positive balance) then how is it stealing for the newcomer to move those BTC to a secure address?

Is ownership over an address justified in a homesteading kind of manner in where the first person to use the address is the owner of that address? For some reason that seems unsatisfactory to me.