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R. Goren wrote a 200 page book explaining his position (linked in Joel K's answer). If you're looking for something shorter and easier, R. J. David Bleich discussed this topic in the first volume of Contemporary Halachic Problems (p. 167 - 176). He summarizes R. Goren's five pronged argument as follows:
Rabbi Goren, claiming to have had additional evidence ...
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You can read Rav Goren’s own explanation of his pesak din here.
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The Mishna (Avos 5:21) says in the name of Yehuda Ben Teima, sets out a study program for Jewish males:
בֶּן חָמֵשׁ שָׁנִים לַמִּקְרָא
בֶּן עֶשֶׂר לַמִּשְׁנָה
בֶּן שְׁלֹשׁ עֶשְׂרֵה לַמִּצְווֹת
בֶּן חֲמֵשׁ עֶשְׂרֵה לַתַּלְמוּד
From the age of five, the study of Mikra (the Hebrew Bible). From age ten, the study of Mishna. At thirteen, he becomes Bar Mitzvah,...
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From the Gemarah it seems that this was a significant issue and fear.
Kesubos 103b;
והיינו דכי הוו מינצו ר' חנינא ור' חייא א"ל ר' חנינא לר' חייא בהדי דידי מינצת דאם חס ושלום נשתכחה תורה מישראל מהדרנא ליה מפלפולי
And this is the background to an exchange that took place when Rabbi Ḥanina and Rabbi Ḥiyya argued. Rabbi Ḥanina said to Rabbi Ḥiyya: You are ...
2
I think the truth is in the middle. It is fair to say that the presence of a machlokes shows there was no halacha l'Moshe miSinai, or else there could not be an argument. And in cases of argument, every Rabbi's ruling is binding on his community. However, the cases of arguments generally were in specific details, while the basic halacha was accepted. The ...
2
The mishna berura writes in hilchos tefilin siman 36 in the name of the kneses hagedola that a person should follow every area of the kabola/zohar that is not in contradiction to halocha. but it is not obligatory
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Commenting on a Talmudic passage (Berachot 3a) in which R. Yosi learned three laws from Elijah the Prophet, R. Zvi Hirsch Chajes essentially asks your question:
ק' ע"ד רש"י (שבת ק"ח ע"א) ד"ה מאי עד שיבא אליהו ויאמר ופירש"י איסור והיתר אין תלוי בו דלא בשמים הוא ע"ש ואיך למד הש"ס דינים אלו מאליהו ואפשר לומר דאם אליהו ...
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The mishna in 10:4 is referring to lighting an oven where the benefit is the heat that is derived after the teruma is already burned, therefore it is only a question of "shvach eitzim" which is only prohibited by things that are issurei hannah. However, teruma is not issur haana and therefore benefit of the heat that is given off is mutar. (See ...
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