A hadith is not the saying of the Prophet as is claimed; the saying of the Prophet is the Holy Quran! Because people say that the hadith is the saying of the Prophet Muhammad ﷺ, and from the Holy Quran, we understand that the saying of the Prophet Muhammad ﷺ is indeed the Holy Quran.
Allah Almighty says: إِنَّهُ لَقَوْلُ رَسُولٍ كَرِيمٍ
Reference: (Surah Al-Haqqah:40)
Translation: Indeed, this (Quran) is certainly the word of a noble messenger.
First Point
There is no consistency between the claim and the evidence because in the mentioned verse, the Holy Quran is referred to as the saying of the Messenger in the sense that you ﷺ are the one who conveyed this Quran to us. Therefore, it is described as the "saying of the Messenger" and not the "saying of the Prophet," because a Messenger is one who delivers the message. Although you ﷺ are both a Prophet and a Messenger of Allah, here the word Messenger is used to indicate that the "saying" is from Allah Almighty and you ﷺ are His conveyor (deliverer).
The Quranic exegete Hafiz Ibn Kathir states: (The term "Messenger" refers to Muhammad ﷺ; its attribution to the Noble Prophet ﷺ is because he is the one who conveys and delivers it. That is why the word "Messenger" is used, because a messenger conveys the message of the sender; although the tongue is his own, the words spoken belong to the sender).
Reference: See: Tafsir Ibn Kathir (14/122), and Tafsir Tabari (23/242)
.But the question is, where does this noble verse prove that the Prophetic Hadith is not the saying of the Messenger? Does accepting the Quran as the saying of the Messenger ﷺ necessarily mean that the Prophetic sayings are not the sayings of the Messenger?
Second Point
What prevents the fact that just as you ﷺ conveyed the Quran to the Ummah through the revelation of Allah Almighty, similarly you ﷺ also conveyed its explanation (clarification and interpretation), the responsibility of which was entrusted to you, to the Ummah?
Allah Almighty says:
وَأَنْزَلْنَا إِلَيْكَ الذِّكْرَ لِتُبَيِّنَ لِلنَّاسِ مَا نُزِّلَ إِلَيْهِمْ وَلَعَلَّهُمْ يَتَفَكَّرُونَ
Reference: (Surah An-Nahl:44)
Translation: And We have sent down to you the reminder so that you may explain to the people what has been sent down to them, and that they may reflect.
The mentioned verse refers to the mission of the Messenger of Allah ﷺ, which was entrusted to you regarding your prophethood, and that is to explain the Holy Quran. So did you ﷺ fulfill that mission or not?! If yes, then what would that explanation be called if it is not the saying of the Messenger?!
Third Point
Every sensible person understands that you ﷺ used to converse with the noble companions, may Allah be pleased with them all, during your life and also guided them. So what would those conversations of yours ﷺ be called? If they are not the sayings of the Prophet ﷺ, then what else can they be called?!
In fact, those sayings of yours ﷺ are called Hadith, which you ﷺ said and upon which the divine revelation is also established.
Allah Almighty says:
وَمَا يَنْطِقُ عَنِ الْهَوَى إِنْ هُوَ إِلَّا وَحْيٌ يُوحَى
Reference: (Surah An-Najm: 3-4)
Translation: Nor does he speak from [his own] inclination. It is not but a revelation revealed.
This noble verse makes it as clear as daylight that the commands of the Prophet ﷺ are also revelations from Allah Almighty.