Is there anybody driving a car that does not use acceleration and braking? I could understand your argument for lane control, but otherwise your argument makes zero sense. Everyone's car is controlled by software, period.
Braking systems are controlled by a dedicated embedded software system that's extremely well-understood and well-tested (probably even formally verified). All it does is check the ABS (and anti-skid) sensors and moderate the braking pressure to avoid locking the wheels. It also has a fail-safe system that gets rigorously tested, e.g. if a sensor fails. All possible values of all inputs are known, and the configurational space of those inputs is small enough that you can exhaustively test correctness.
It's plainly obvious that a braking system controller software is a very different beast from an autonomous car software, and I have no problem understanding why someone would trust th former and not the latter.
> Braking systems are controlled by a dedicated embedded software system that's extremely well-understood and well-tested (probably even formally verified).
Are you sure? That code is closed source, and the peek behind the curtain we saw with Toyota's investigation did not inspire confidence:
That's a really interesting article for sure. But it does highlight that Toyota was being unusual in not following industry-wide (voluntary) coding standards for safety-critical embedded systems in cars, and they ended up losing big in court. So I do think (hope) that this example is worst-case, not normal.
The person you were replying to was talking about adaptive cruise control and automatic breaking. The majority of cars on the road do not have those features. Very different than plain acceleration and braking and much more likely to have glitches.