How can one show that Islam means peace when Muslims are fighting?
By distinguishing between teaching and practice. As long as Muslims lived by Islam, they rose; their present state does not show Islam, but how far they have moved away from it.
The question is a fair one. Anyone looking at the Muslim world today sees conflict between groups and a great deal of moral decline. An outside observer can hardly believe that the reality of Islam is different. A simple yes or no will not do here. It needs a clear line of thought and examples.
The key is the relationship between a teaching and acting upon it. If a teaching is good, people rise as long as they live by it, and they fall when they turn away from it. If a teaching is bad, the opposite happens. People do better as soon as they leave it behind.
In the case of Islam, history shows the first pattern. In the early centuries Muslims largely lived by their faith. That was exactly the time when they rose to greatness, wisdom and learning, and many non-Muslim historians acknowledge this. When they turned away from Islam, their decline began. So their present condition is not the result of Islam, but of abandoning it.
The history of Europe shows a different picture. The period when the Church governed the whole of life is called the Dark Ages by European historians themselves. The awakening came with turning away from it, and it was named the Renaissance, a rebirth. Today’s Western civilisation largely sees itself as secular.
Whoever understands this connection can convince a reasonable person. Islam should be judged by its teaching and by the time when that teaching was lived. The hadith above gives the measure by which every Muslim must be judged, which is whether others are safe from his words and deeds. If someone is determined not to accept this, you are not responsible for him.