Well accomplishing that will surely require a lot of mental discipline, and I can see it is related to seeing reality in an objective way am I right?

Yea...it is takes a lot of mental discipline. But it get easier. And yea, like looking at events objectively, from the perspective of others.

Being indifferent to pleasure is particularly quite hard, because a lot of people would think that our reason to live is to be happy, which can be considered as something pleasurable.

Pleasure in this context is attached the 'external'. One can derive pleasure by eating good or getting a new toy. It makes him happy for a limited time, then he is on to getting a new one. Happiness should come from within. Marcus Aurelius, an emperor, one of the famous stoic philosopher, talked about meditation. It is a way to get away from the external for a while, it helps keep your mind and soul at rest, and refreshed.

What is the reason to live according to Stoicism?

The first thing is for one to be at peace himself, free from uneccessary negative emotions that help nobody's cause. Applying ethics and logic will help achieve true happiness and be in harmony with nature (the world around him).