What are the arguments for and against giving special status to the Spanish language in the United States ?
To begin with, I do not know of any attempts to give Spanish a "special status" in any official way. There are places where official information is printed in English and Spanish, but there are also places where such things are printed in many other languages as well. If you would like to clarify what you mean by "special status" please do so.
The only reason for giving Spanish special status would be to recognize that Spanish-speakers are a significant minority in the United States and to make it easier for them to function if they are not fluent in English.
The arguments against this are much more numerous. First, if we were to have an official language, it would surely be English since that is the language spoken by the vast majority of Americans. Second, giving Spanish a special status would slow the process of assimilating Spanish-speaking immigrants and their descendants into mainstream American society. Giving Spanish a special status might lead to the sorts of problems that Canada has with separatists in Quebec.