How is taproot address not safe against quantum computers if it is not resused for transaction?
He is trying to tell you how your Bitcoin isn't safe from Quantum computers if you are using a taproot address to keep Bitcoin for long term.
When you send a transaction to other type of address, like native segwit, legacy and nested segwit, the transactions are visible on the blockchain network but the only thing you can see from the scriptpubkey is only the hash160, the public key will not be visible until the Bitcoin is ready to be spent which must be provided by the spender(both the signature and public key).
The two conditions that can reveal the public key is if you spend the output or spend part of the output. This is why it's not recommended to reused an output, it should be spent once because the public key to that address is already visible.
Contrary to taproots, when an outout is spent the pubkey becomes visible to the public, anyone can see your public key and that's a threat to everyone that are keeping Bitcoin for long term using taproot address.
He is suggesting you move your Bitcoin from taproot address to native segwit address prior to when Quantum solution will be available.