What authority does China have to declare that Tibet is China? Taiwan? Everything inside the 9-Dashed-Line? What reason do we have to accept China's authority to declare that foreign territory is in fact part of China?
In the same way, when the bank robber says that he was just withdrawing his own money, we do not accept that the bank robber has authority to declare "what is rightfully his money".
China has dejure claims over Tibet and Taiwan. So it's more like a person who legitimate has access to their bank account wants to make withdraws after not touching the account for a while. But some nosy folks are butthurt because they falsely think it's black money or there's some mythical expiration date on legal ownership, tries to paint it as such, goes out of the way to prevent it, even though lawfully PRC is in the clear. SCS is an inheritance dispute, which other parties decided to involve arbituation that China didn't accede to.
But the practical answer is, under Westphalian order whose principles are enshrined in UN Charter (again the organizing order post war), PRC has authority to declare whatever she wants within her domestic jurisdiction, of which Tibet and Taiwan is formally recognized to be part of. UN has no position on legal/procedural merits PCA/UNCLOS ruling for SCS. That's a messy situation that gets resolved same way all territorial problems in Westphalian order gets resolved in lieu of treaty/accord that formally assigns ownership, territorial control with lots of force. So Chinese authority is derived from the same post war order as everyone else.
In the same way, when the bank robber says that he was just withdrawing his own money, we do not accept that the bank robber has authority to declare "what is rightfully his money".