How to argue with your professor
If you want to know how to win an argument, then you may need to re-examine your current understanding of an argument. The idea is that two or more people share ideas until either one argument appears stronger, or the argument(s) are equally valid or invalid. Winning an argument is only important if you are right, and the only reason you think you are right is because somebody hasn't yet put an argument across that swayed you.
The reason many people wish to learn how to win an argument is because they come across people that ignore and/or do not demolish their arguments. If you raise a point, and the other person demolishes the point, then that is okay, but if the other person simply moves on and/or ignores your point, then you cannot win. If you are dealing with a stubborn arguer, you may have to be stubborn back and keep raising your point until it is addressed. If it is addressed correctly, then you may have to concede and move on. Fortunately, if you are part of a written debate or discussion, you can reach out to the professionals from the assignment masters. They will help you to choose and to present your argumentation in the best possible way.
Be wrong and change every time
If you wish to know how to win every argument, then you have a lot of growing up to do because only juveniles and intellectually subpar people wish to win every argument. The most intelligent people will welcome being proven wrong because it means they may evolve and change. The whole point of arguing with a superior intellect is so you may adjust your own arguments, even if it means creating contrary arguments to what you originally believed.
Do not label
If you label people, then you are proving you are intellectually anemic and unable to defend your own arguments. People label others so they have an excuse not to argue with them (because they are unable to do so correctly). Instead of taking part in a sensible argument, a person will label the other person with something such as "Racist" or another word of that ilk so that he or she doesn't have to argue, after all, who wants to argue with a racist?
The most commonly used labels that intellectually anemic people use are Sexist, Intolerant, Xenophobic, Homophobic, Islamophobic, Racist, and Bigoted. If you use any of these labels when arguing with others, then you are no different to the clueless, outwardly upset and loud college student with no life experience and no perspective on reality other than what mummy and professor has engineered for him/her.
Be prepared to agree to disagree
It is hard to understand, but there are times when nobody is wrong, and there are times when nobody is right. It is possible for two completely opposite opinions to be correct. A person who contends that god exists may be just as correct as a person that says god doesn't. Even in that case, an omnipotent being is able engineer its own none existence in a universe where the concept of time exists. Two people can be right at the same time, for example, think of the decades where people argued that light was a wave and a particle, and then it turned out that light is both.
Embrace and ignore every label you are given
Dullards are going to throw labels at you because they are unable to argue with you. They may do it through laziness, but it is usually through pig ignorance. The worst thing you can do is try to fight the label because you shift the focus from the point you are making to the label itself. Remember that you have to be stubborn if you have an argument point that is not being addressed by the other person. Simply say, "You have no right to label me..." and then go right back to the point you wish the other to discuss.
Do not fool yourself into thinking that your professor will not label you because he or she will. However, the sad fact is that your professor is the one that marks your work, so it is probably best that you simply agree with your professor and write whatever ideology he or she wishes because you will only fail otherwise. Keep your correct arguments and opinions quiet until you leave the free-speech death camp that is college (where students are even being punished for free speech in safe zones).