How do context, personal experience, and unspoken assumptions affect the way people express reasons & conclusions?
This is a very sophisticated question. Let me give you a few points to consider.
First, social scientists such as Foucault and others have clearly shown us that people know things in the mode of the knower. In other words, we know things through the lens of our personal experiences. Hence, there is no such thing a objective reality. Our conclusions and convictions are rooted in our personal experiences.
Second, another very important point that social scientists have made is that each society or culture has a certain commonsense view of the world. In other words, each society has shared assumptions. For example, if you were living in India, you would believe in many gods and this would not be incompatible with science. However, in parts of Europe you might be inclined to be more skeptical, or to hold a view that science and religion are incompatible. Hence, people are profoundly affected by their social environments. This has a profound effect on people's conclusions. I will link an excellent book on this topic.