An "assertive" person is someone who strongly states and fights for their own opinions. A good image for the word "assertive" is a person who is able to ask their boss for a raise when they think they deserve it.

The word "assertive" has a positive connotation. You can often hear people telling their children or spouses:

You should be more assertive!

But it's not strongly positive. People want to have this quality for themselves but might find it a little annoying when other people display it. So in the example above, the speaker is able to use this as an example of a "weakness".