There's two realities here.

1) The Righteous approach: you take your grade back to the professor in his office at a scheduled meeting. Armed with a clear head you argue your case, and demand apology for his condescending attitude. If he doesn't budge, inform him you will be taking the matter to the department head. Be transparent and firm, you deserve a proper grade and you have nothing to hide. You may have a low probability of success with the dept. head, as my experience has been they will generally defer to the professor's judgment unless there's pre-existing strain on that particular professor's credibility with the department. But at least you've made your case and can produce documentation should it ever be required. You may choose to mention the professor's attitude, but I'd recommend against it unless he's already on thin ice for student relations. You'll have to deal with assholes in positions of power your entire life, the sooner you learn to deal with it on your own the better off you'll be.

2) The Realistic approach: you must weigh the benefit of outcome to the costs. Fighting this issue could sour your relationship with the professor and is likely to influence your future grades. This is especially true with subjective disciplines, such as one in which a professor reserves the right to arbitrarily dock grades on principle. How much will this affect your overall average? Will it realistically have any significant impact on your job prospects, or is it simply a pride issue? I can tell you, the moment I signed my first offer acceptance letter out of college the minutiae of my transcript stopped being relevant. From then out, all that mattered was the mere existence of that degree (and the granting institution) + relevant experience. This little hiccup in all probability has precisely zero impact on your life. Let it go, learn what the professor expects, justified or otherwise, and excel on his terms. You will be doing exactly this for the entirety of your professional life until you work for yourself so, again, the sooner you can do this the better off you'll be.

Good luck