Jesus does not seek a quarrel with the Pharisees but they, of course, are proactive in pursuing him. Upon hearing the news of this remarkable healing, they come after Jesus ready to accuse him of not simply being a Sabbath-breaker but of being in league with the Devil himself. While the multitudes are discussing whether Jesus could be the Son of David, the Pharisees are saying, "This man casts out demons only by Beelzebul, the ruler of the demons." That's quite an interesting spin on what just took place here. Jesus commands the demons, therefore he must be their leader, their commander-in-chief. The Pharisees' twisted minds come to the exact opposite conclusion as the crowd.
Jesus answers, "If Satan casts out Satan, he is divided against himself. How then shall his kingdom stand?" A general would not order his army to attack their home city that they are trying to defend. Likewise, if Jesus is commander of Satan's army as Satan's servant, why would he order an attack on Satan's kingdom? Is Satan divided against himself? Obviously, Satan would not cast himself out of a man. That would be like beating himself back out of conquered territory. He would be working against his own purposes.
And the Pharisees know this because even their own disciples perform exorcisms that aren't called into question. This is what Jesus means when he says, "By whom do your sons cast them out?" "Sons" refers to followers or disciples of the Pharisees. Do the Pharisees accuse everyone who casts out demons as being a servant of the Devil? No, just Jesus. And that's the point. Someday on the Day of Judgment, the Pharisees' disciples will be called to testify to this fact against their mentors. The Pharisees' accusations are clearly prejudiced against Jesus, because if he really is casting out demons by the Spirit of God, they might actually have to listen to him.
"Or how can anyone enter the strong man's house and carry off his property, unless he first binds the strong man? And then he will plunder his house." Jesus compares Satan to a strong man who occupies a person's body as if it were his own house. The strong man must first be overpowered and tied up before you can plunder his house. Only the Spirit of God can overpower Satan in this way. So, obviously, Jesus casts out demons by the Spirit of God, which means that the kingdom of God has come upon them.
I think it's interesting to note that Jesus makes these arguments assuming that Satan is not a blundering idiot, nor a weakling you can trifle with. Satan would not make the tactical mistake of undermining his own kingdom, nor can he be expelled by any power short of God himself. You might even say that Jesus has a healthy respect for his cunning and resourcefulness; and you can be sure it is on the forefront of his mind every day as he battles Satan's attacks, coming to him in the form of demon possessions, hypocritical authorities, hostile Gentiles, unbelieving hearers, hard-hearted disciples, and two-faced friends.