There are many reasons why Catholics and other Christians believe that social justice in an important work. Let me give you a few of them.
First, Catholics believe that social justice is part of what they are called to do as followers of Christ. One of the things that Jesus did on earth was to seek social justice. For instance, he welcomed the socially marginalized and loved them. He healed lepers, welcomed prostitutes, and cared for those who could not take care of themselves. Vatican II put these points into their official teachings. I will add a link on this topic.
Second, Catholics believe in the strong moral teachings on this topic from places like the Book of Amos. In other words, they believe that social justice is part of their divine mission. Here is a brief except from the Book of Amos:
“I hate your festivals, nor do I delight in your solemn assemblies. Even though you offer up to me burnt offerings and your grain offerings, I will not accept them; and I will not even look at the peace offerings of your fatlings. Take away from me the noise of your songs; I will not even listen to the sound of your harps.But let justice roll down like waters and righteousness like an ever-flowing stream.” Amos 5:21-24.
Finally, Catholics commit to social justice to be a witness of the love of God in the world. All you need to do is think of someone like Mother Theresa.