Stoicism is a philosophy about how to live well. The central tenants are the cognitive model of emotion, the dichotomy of control, and the focus on virtue.
Why should you believe it? Note that Stoicism itself demands that you not accept it on faith. You should only believe what you have good reason to believe. Note to that, just as there are different versions of other philosophies, there are different versions of Stoicism. The important part is that it's up to you to determine what is true.
The primary idea of Stoicism is that virtue is what is ultimately value. This means, when making decisions, decide with courage, justice, and wisdom. Don't sacrifice acting with courage for the sake of personal gain or comfort.
If you place your hopes for a good life in material success or some other external, then the value of your life is out of your control. Life is uncertain and random. The value of your life will be held hostage by the world and is out of your hands.
If what is ultimately value is under your control, you will not have this problem. Whether or not you live a good life is your responsibility and yours alone.
This is why Stoicism is true. Because it places the ability and responsibility of living a meaningful life entirely into your hands.
Note how the idea of the dichotomy of control plays a role here.
Let’s consider an objection.
Does Stoicism fail to capture the value of meaningful relationships? Aren’t they a part of the meaningful life? But aren’t they also external? It is true, one one hand they are external. People are finite and make their own decisions -- one cannot control them. It is important to realize this. However, cultivating virtue is crucial for obtaining other goods, such as good relationships. If you are virtuous, you will attract the virtuous. Far from hampering the pursuit of other values, like meaningful relationships, Stoicism enable it.
So, the focus on virtue puts the value of one's life under one's control and is necessary for obtaining other good parts of a life. What we need to do is focus on what we can control, embrace reality, and act with excellence.