Based from the website https://www.skillsyouneed.com/ps/assertiveness.html Being assertive means being able to stand up for your own or other people's rights in a calm and positive way, without being either aggressive, or passively accepting wrong.
So to answer your question, no assertive communication does not mean to persuade others to agree with your point of view, it just means to stand up for what you or other people believe in.
