It's a rhetorical bit of three card monte. Note that he seamlessly shifts from pursuing an absolute of bug-free software and instead offers some techniques for reducing bugs, which the manager deems more expensive than the gains they'd offer. Then he conflates "would be better" with "bug-free software" in a bit of snark at the end, and you can almost hear the eye-roll from the manager.
The main problem about unit testing is that you only can demonstrate that the software pass all your unit tests not that the software is bug free.
Also, your software usually run on top of other layers that you need to trust like the operating systems, VM, BIOS, hardware failures...