Freelance writing is a challenging work, and if you are in the field for long then you are bound to come across one or two angry client. Therefore, you need to know to handle the situation should your client gets angry on something — you are lucky if you have not get one, still you need to know the tricks to handle rough weather in freelance writing.
If your client is angry of you then try to find out the reason for his anger. Do not just judge the situation from your point of view only. You may be right, but it is the client who has to decide if he liked your work or not. After all, he is in better position to say whether your article or content will meet is his goal or not.
No one wins the argument, so do not invest time in that. Let your client do the talking. This will help you understand his point of view, and will also vent his anger out. Do not interrupt, and speak only when he is done. Afterward, patiently explain everything, and logically build you case and tell him why you think the content in question will work.
Do not fight over the content, if you do not wish to lose that client. If your client is not satisfied by the output, offer a rewrite. Tell him you will rewrite everything to meet his expectation, and before you do that ask him about his particular requirement, in terms of style, presentation, and structure of the content that you are supposed to rewrite. Take every step necessary to remove the ambiguity from the project. This will help you rewrite it.
If your client’s anger is just then this will pacify him, and if it isn’t then you cannot do anything about it. But still, you should try to understand his point of view and solve the issues he has.