First, let's try to define both explanation and generalisation.
Roughly speaking, it is a series of statements designed to shed light on a supposed matter of fact.
An explanation is composed of two things: the explicandum and the explicans.
The explicandum → the fact, thing, or expression which is to be explained.
The explicans → the explanation given for a fact, thing, or expression.
Smoke appears because of fire: a combination of flammable material,
oxygen, and sufficient heat.
Smoke appears is the explicandum and
fire: a combination of flammable material, oxygen, and sufficient heat is the explicans.
Roughly speaking, this is a broad statement or an idea which is supposed to
apply to a group of things.
The customer is always right
It seems to me that a generalisation such as the above can be part of the explicandum but it shouldn't be part of the explicans because, ideally, it would require an explanation of its own.
This is of course assuming that you want your explanation to be a good one.
In this sense, a generalisation doesn't quite fit the explanation criteria.