Here is the rule: "Do no harm."

Why should we follow it?

A rule-consequentialist would say, "Because if everyone followed that rule all the time it would lead to better consequences, on average, than if people tried to calculate the consequences of each individual action and act to maximize them."

Why would that lead to better consequences?

A rule-consequentialist could say, "Because people are quite bad at calculating consequences, especially in the tumultuous time before making a critical ethical decision. While we have had the time to think and properly calculate the hypothetical consequences of everyone following the rule."

I think that's exactly the argument Eliezer is making.