Some thoughts on disagreeing with other people:
1. Whenever we express disagreement with someone else, our goal should always be to speak the truth in love. If we have a motive other than love, we have the wrong motive. In other words, our goal should be to edify, not to build up ourselves or to tear other people down. This means that our intellectual posture should be one of love, grace, and humility.
2. We should recognize that the person we disagree with is a human being that God has created in His own image. We thus have a major responsibility not to sin against that person, and in this case, not to bear false witness against that person. We must portray the person's argument accurately and fairly, and we must show the other person the respect and dignity that he/she deserves as a human being, no matter what. Because human beings are sacred, we must disagree in a sacred way. Christ Himself commanded us, "Love your enemies." We must make sure that we are not attacking the person but the specific points of argument that we believe are incorrect.
3. When we disagree with another person, we should make sure we have a clear, accurate idea of what the other person is saying. We should have listened to the other side carefully, noting their lines of argument, their specific evidence for their position, and their logic. We should see how much support they are providing for their position, and find the specific points where they are wrong. We should never attack someone if we haven't listened to them carefully in the first place. If we have tuned out the other side's case for their position in its entirety and in the details, we have no right to attack them.
4. We should never simply assert that the person is wrong without giving any evidence for this assertion. Instead, we should support our claim with specific evidence from the other person's argument. To simply claim that someone is wrong without giving any specific evidence to support our assertion is not fair to the other person as a human being. We shouldn't be sloppy in our critique, but specific and precise. As Dryden put it, "there is still a vast difference betwixt the slovenly Butchering of a Man, and the fineness of a stroke that separates the Head from the Body, and leaves it standing in its place."
5. We should portray the other person's position fairly and correctly. If we claim that the other side holds a certain position, but our opponent wouldn't agree that our portrayal of his position is accurate, we have misrepresented him. Our opponent should say, "Yes, you have portrayed my position correctly." To do otherwise is misleading and, worse, committing the sin of bearing false witness against our neighbor.
6. We shouldn't make a public or online accusation without any attempt to speak to the person privately first. Once again, our opponents are human beings that God loves, and we should treat them as such. We should do unto others as we would have them do unto us if we were the ones in the wrong (and every one of us is wrong sometimes about some things). Every one of us would rather have a person come talk to us privately before posting an online attack of our position without first speaking to us face to face (or email to email, etc.).
It is not wrong to disagree with someone. In fact, disagreeing is often the right thing to do. The challenge for a Christian is to disagree the right way--a way that shows love for God, reverence for precise truth, and love for people on the other side, affirming them as human beings created in the image of God—even if they are wrong about something.