When do you need to make your essay argumentative? When the topic is controversial and you have to show your stance with good support, it is not enough just to present your one-sided arguments. You need to take into account the opposing views. You have to mention the counter-arguments and to refute them.
Let's work on the following topic which is obviously controversial and see how we can make a good argumentative essay out of it.
Some people think that animals should be treated the same as humans, but others don't. Write an essay, saying whether you are for or against such a view.
Approach
Before you write, you have to decide on your stance.
Let's say you agree that animals should be treated the same as humans. You have to give three reasons why you think so.