Rambam- Yesodei HaTorah- Chapter 9 Halacha 4: Prophets Do Not Decide The Law, For 'It Is Not In Heaven!"

וכן אם עקר דבר מדברים שלמדנו מפי השמועה או שאמר בדין מדיני תורה שה' צוה לו שהדין כך הוא והלכה כדברי פלוני הרי זה נביא השקר ויחנק. אע"פ שעשה אות. שהרי בא להכחיש התורה שאמרה לא בשמים היא. אבל לפי שעה שומעין לו בכל:

So too, if the prophet contradicts something that we learned from an oral tradition or says one of the laws of the Torah is [a specific way] because G-D commanded him that the law is so and the law follows so-and-so's opinion, this is a false prophet and he should [be put to death] through strangulation. [This is true] even if he performs signs since he came to destroy the Torah, since it says(Devarim 30:12) "It is not in heaven." However, we listen to him with all [commandments that are to last] for a finite amount of time.

Why is it so bad for a prophet to tell us which Rabbi to side with? He is not telling us a new law, only telling us which one of the Rabbis is favored by G-D. Why should this lead to him being put to death? One answer is given by the Maamer Mordechai:

לא בשמים היא וכו'. נ"ב אין להקשות ממ"ש בריש הפרק ויאמר שה' שלחו להוסיף מצוה וכו' דמשמע דוקא כשבא להוסיף או לגרוע הוא דנקרא נביא השקר אבל באומר הלכה כפלוני (דאיהו) [דאינו] מוסיף ולא גורע לא דהא גם הכא הוי שינוי דהא כיון דכתיב לא בשמים היא א"כ גם אינה בשמים להכריע הדין עם מי וא"כ כשזה בא ואמר הלכה כפלוני ואומר שה' שלחו א"כ נמצא דמכחיש כתוב דכתיב לא בשמים היא והכי דייקי דברי רבינו ז"ל ועיין בכ"מ ובפר"ח ודוק.

It is not in heaven, etc: This requires explanation. One should not ask based on what it says in the beginning of the chapter "The [false prophet] will say that G-D sent him to add a law, etc." That this seems to imply specifically when the [false prophet] tries to add or take away [a law] that he is called a false prophet, but if he says the law follows so-and-so, that [the false prophet] is not adding or taking away [a law, he is] not [put to death.]   This [is faulty reasoning] because [a prophet telling us which Rabbi to follow] is a change [from normative Jewish practice] because it is written (Devarim 30:12) "It is not in Heaven." Therefore, it is not in heaven to decide who the law follows. If so, when this [prophet] comes and tells us, "The law is like so-and-so," and he says, "G-D sent me," we find that he is extinguishing the verse that writes (ibid), "It is not in heaven." This is the reasoning of the [Rambam]. 

The Torah tells us that no one is allowed to add laws or subtract laws from the list of commandments. However, the verse (Devarim 4:2) "You shall not add to the word which I am commanding you, nor take away from it, that you may keep the commandments of the Lord your God which I command you," only tells us that the prophet is not allowed to come and make up a new commandment. From where do we know that their status as a prophet has no authority over us in any matters of permanent law? That comes from the verse (Devarim 30:12) of "It is not in heaven." This verse teaches us that once the Torah was given, the Rabbis now have authority over the law and not G-D. Human logic and reasoning is how we decide matters and not through divine intervention. This is a foundational principle of Judaism and must be understood. The majority rules what is law, not G-D. As demonstrated in Babba Matzia 59b by the oven of Aknai as was described in the previous mishna.