It does say that.
Since you are so wise and know God so well, let us discuss this further, okay?
John 6:63 The Spirit gives life; the flesh counts for nothing. The words I have spoken to you--they are full of the Spirit and life.
Is not the same as
The Word is the Spirit.
The Person of the Trinity known as the Word is not the Person of the Trinity known as the Spirit.
A person is not spoken words. Spoken words are not persons.
Spoken words being full of the Spirit and life means that the words spoken by the Word are full of the Spirit and of life. The verse is simply not saying what you are trying to make it say.