Often a strong willed child could be confused as a child acting out, pushing buttons, just plain naughty!
A strong willed child is non of the above, they are however prone to power struggles.
A demanding voice, will not get you what you want, however a little negotiating will go much further.

Understanding a strong willed child is needed in order to know how to parent one.
Strong willed children do not want to submit to another person, can not lose an argument, they cant lose face!
They are leaders… and need to be recognized for that as a skill, not a burden.

Your child may invite you to attend an argument daily, you have the choice to attend or to leave well alone.
As the adult I suggest you pick your battles and approach with care. Your strong willed child could have you acting like a five year old in no time at all with back and forth banter.
Learn to negotiate, and learn how to ask rather than demand.

1) Avoid power struggles with a routine ( reminders, rather than demands, remember we always pick up the toys before we sit down for dinner.

2) Give choices, this will make him feel he is more in charge of his own destiny.
Do you want to do your homework now, or after dinner?

3) Allow your child freedom as much as possible, never putting safety in jeopardy of course.
If you put your lunch bag in your back pack, you only have carry one bag,  but if you prefer to carry two that is fine also.

4)  See situations from his side. You said you would take him to the movies after school, now your home late and have missed the movie. You made a promise, and broke it, if he broke a promise he would sure hear about it!! Apologies and find a way to make it up to him.