Romans 15:4 For whatsoever things were written aforetime were written for our learning, that we through patience and comfort of the scriptures might have hope.Like the Old Testament, the New Testament is the Word of God - the Holy Spirit inspired it. It is the revelation of Jesus Christ by the Holy Spirit according to the will of the Father. As it is written:
Luke 24:44 And he said unto them, These are the words which I spake unto you, while I was yet with you, that all things must be fulfilled, which were written in the law of Moses, and in the prophets, and in the psalms, concerning me.
John 12:16 These things understood not his disciples at the first: but when Jesus was glorified, then remembered they that these things were written of him, and that they had done these things unto him.
Revelation 1:1 The Revelation of Jesus Christ, which God gave unto him, to shew unto his servants things which must shortly come to pass; and he sent and signified it by his angel unto his servant John:So, specifically the book of Revelation was a revelation given by Jesus to John (that addresses Meyer's sub-objection that "we don't even know if he told his followers to write anything down, and often it seems they dont expect it to be scripture anyway"), and more generally what Paul taught was revealed to him by Jesus. But what about Scripture generally?
Romans 16:25 Now to him that is of power to stablish you according to my gospel, and the preaching of Jesus Christ, according to the revelation of the mystery, which was kept secret since the world began,
Ephesians 3:3 How that by revelation he made known unto me the mystery; (as I wrote afore in few words,
Galatians 1:12 For I neither received it of man, neither was I taught it, but by the revelation of Jesus Christ.
2 Timothy 3:16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:And not only is it inspired by God, but God is indeed the reason for Scripture's existence:
2 Peter 1:19-21So, the Scriptures come according to in the inspiration of God the Holy Spirit and he speaks what Jesus spoke:
We have also a more sure word of prophecy; whereunto ye do well that ye take heed, as unto a light that shineth in a dark place, until the day dawn, and the day star arise in your hearts: knowing this first, that no prophecy of the scripture is of any private interpretation. For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost.
John 14:16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;Thus, the New Testament is the revelation of Jesus Christ by the Holy Spirit, as it is written:
John 14:26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
Hebrews 1:1-2I'd love to write more, but hopefully this answers the objection thoroughly - Jesus in his humanity did not write a book, but he sent the Holy Spirit by whose inspiration his oral teachings were brought to remembrance and memorialized in Scripture:
God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets, hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;
Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us, even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word; it seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order, most excellent Theophilus, that thou mightest know the certainty of those things, wherein thou hast been instructed.
And many other signs truly did Jesus in the presence of his disciples, which are not written in this book: but these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.