Why Owner 1's Signature is in transaction #2, not #1 In Bitcoin, what is the Signature and why Owner 1's Signature is in transaction #2, not #1?

I'm implementing a demonstration of blockchain database. But I noticed that the Bitcoin whitepaper has many ambiguous things, such as what is a hash of previous transaction of the first transaction. But the hash problem seems to be resolved somehow. The problem is what is the signatures and why it exists in next transaction of its owner issued?
Owner #1's signature is required for Transaction #2 because Owner #1 at that point owns the bitcoin. It's being signed over to Owner #2.

Think of it this way, who signs a USD check where money goes from #1 to #2? It's always whoever owns the money beforehand.