What does it mean that in a fully non-custodial protocol, you are solely responsible for your funds?

A real-life example happened on Oct 30, when dYdX v3 gave way to dYdX Chain (v4). The old Layer 2 exchange was frozen and all open positions were valued at oracle prices at the time of the trading halt; since the state of all accounts is stored on the Ethereum smart contract, the users' funds will henceforth remain available for withdrawal indefinitely, without the need to rely on dYdX Trading or any other party for redemption!

So who do you trust the most? Ethereum or your bank?

Crypto native, web3 wanderer, DeFi chemist and metaverse voyager.
Empirical reality can be operated by streams of bits and chains of blocks.

And you, which folk would you rather be? The one that is in control of its own wealth or the one that entrusts it to a corporation?

Well, different strokes for different folks

I prefer the former, to be honest. There are risks associated with this option, though.