A significant portion of the Qur'an is devoted to narrations of Muhammad's arguments with his opponents. But if his message was peace and love, why did he even have opponents? The long answer to this question begins with a brief overview of the cultural and historical context to which Muhammad introduced the Qur'an.
You may know of Mecca, the Holy City of Islam, in western Saudi Arabia. You may know of the Ka'aba, that large, black structure in Mecca that looks like the Borg from Star Trek. It is a shrine to Yahweh, the Muslim god, the god also worshiped by Jews and Christians. You may know of the pilgrimage and circumambulatory ritual performed by countless Muslims every year at the Ka'aba. The Ka'aba, the pilgrimage, and the ritual were all there long before Muhammad.
The pagan Arabs respected Yahweh, and even acknowledged him in their prayers as the Supreme Being of All Things. But they were modest about their place in the cosmos: not wanting to bother the Big Guy with their mundane problems, they turned instead to idols, lesser deities who served as intercessors with Yahweh. In Muhammad's day, although it was nominally devoted to Yahweh, the Ka'aba hosted several hundred idols that received quite a bit of the pilgrims' attention.
While the men of Muhammad's culture spent a lot of time at war with each other over matters of family honor, they usually respected the tradition that violence was never allowed anywhere near Mecca. This paid off--not only for pilgrims, who could focus more on worship and less on their personal safety, but also for Mecca's cash-flow. By Muhammad's time, some of the families of Mecca had grown wealthy, to some degree due to the periodic influx of hungry, thirsty pilgrims.
By custom, certain tasks relating to pilgrim hospitality and guardianship of the Ka'aba were managed by two officers from the leading tribe of Mecca. Great prestige was associated with these positions. One indicator of the importance of family honor is that the various clans of this tribe were willing to march themselves outside the no-fighting zone to slaughter each other for the privilege of fielding these officers.
Now, let's recall our question: why did Muhammad have opponents? It certainly was not because of his message of peace and love; that is not what the Qur'an is about. If you've been following this series, you've heard my summary of the Qur'an's message. Muhammad's version goes like this: Yahweh is the only god; the idols are inanimate objects, not gods. Yahweh is furious that people talk, or rather, think they're talking, to any god other than himself, so furious that no matter how much good you ever do in the world, if you don't repent of your engagements with other gods, you will go to hell.
Muhammad wanted to destroy the idols. Needless to say, this would be a blow to the pilgrimage industry, and Muhammad tried to make it seem that the greed and arrogance of the wealthy were behind much of the opposition. But it wasn't just the wealthy who would have been affected. The loss of the pilgrims would have shaken all of Mecca's economy. Muhammad conveniently overlooked this point.
Further, the naysayers were far more genuine than he gave them credit for, and it is truly poetic justice that his own descriptions of their arguments give the lie to his insinuations. Their fear of economic downturn was minor compared to their fear of each other. If the tribes of Mecca were to let Muhammad have his way, their rivals outside Mecca would invade the city and drive them off their land for allowing the Ka'aba and the idols to be desecrated.
Surprisingly, these material concerns were only a small part of the pagans' complaints against Muhammad. Most of the their comments reflect more of a gut-level reaction, which leads us finally to the short--and obvious--answer. Why did Muhammad have opponents? His listeners were simply offended by his derogatory pronouncements, which amounted to: you're a bad person. God has chosen me specially to tell you so. Your cherished family traditions are repugnant. And if you don't do what I say, you're all going to hell, along with your esteemed forebears who gave you those traditions.
Why did Muhammad have opponents? Because he went around insulting people, their customs, their families, their ancestors. And yet, he now has followers who will kill you for drawing his likeness.