Questions about example sentences with, and the definition and usage of "Assertiveness"

A: "leaves much to be desired" as a phrase means that something is lacking, or that there isn't enough of it. Assertiveness means confident, in control, or powerful. Therefore, person speaking thinks the other person is not confident enough.

A: Her smile was obviously fake.

One of his key traits was his assertiveness.

The jacket was a fake.

A: One can be confident without being assertive, picture some guy who's sure of himself, his capabilities and what he wants in life, but not trying to impose his own views and values onto those around him. But one cannot be assertive without being confident, because assertiveness necessarily requires one to impose upon others, at least a little bit.

A: is it ok ?