Explanation why dc-dc converter is a time-variant system
I believe this is a mainly subjective question.

We have different models with different characteristics to represent the same thing in nature. Different models are useful for different goals.

We have the definition of time-invariance in terms of differential equations, and it involves using a model.

So, in the case of a DC-DC converter, you could have a time-invariant averaged model and say that it "is" the converter itself.

In the other extreme, pretty much everything could be represented as a time variant, non-linear system, if we have a sufficiently complex detailed model of it.

So in my opinion there is no right answer for it. It could and it could not. If you have a model with different equations depending on the state of the switching devices, then yes.