Why I believe Paul did not write Hebrews

2 Thess 3:17

The salutation of Paul with mine own hand, which is the token in every epistle: so I write.

If you look up the word "salutation" in the dictionary, you'll find a definition that goes something like this: 

SALUTATION: 

- word of greeting used to begin a letter opening 

- the initial part of the introduction.

While we today sign our name at the bottom of letters we write, that's not how epistles (i.e., letters of instruction meant to teach, as from a teacher to a student) were written.

Rather, verse 17 is instructing us that Paul is the author of the epistles, Romans-Philemon.  Those are the only books that contain his name in their introduction, as shown below.

Romans 1:1
PAUL, a servant of Jesus Christ, called to be an apostle, separated unto the gospel of God,

1 Corinthians 1:1
PAUL called to be an apostle of Jesus Christ through the will of God, and Sosthenes our brother,

2 Corinthians 1:1
PAUL, an apostle of Jesus Christ by the will of God, and Timothy our brother, unto the church of God which is at Corinth, with all the saints which are in all Achaia:

Galatians 1:1
PAUL, an apostle, (not of men, neither by man, but by Jesus Christ, and God the Father, who raised him from the dead;)

Ephesians 1:1
PAUL, an apostle of Jesus Christ by the will of God, to the saints which are at Ephesus, and to the faithful in Christ Jesus:

Philippians 1:1
PAUL and Timotheus, the servants of Jesus Christ, to all the saints in Christ Jesus which are at Philippi, with the bishops and deacons:

Colossians 1:1
Paul, an apostle of Jesus Christ by the will of God, and Timotheus our brother,

1 Thessalonians 1:1
PAUL, and Silvanus, and Timotheus, unto the church of the Thessalonians which is in God the Father and in the Lord Jesus Christ: Grace be unto you, and peace, from God our Father, and the Lord Jesus Christ.

2 Thessalonians 1:1
PAUL, and Silvanus, and Timotheus, unto the church of the Thessalonians in God our Father and the Lord Jesus Christ:

1 Timothy 1:1
PAUL, an apostle of Jesus Christ by the commandment of God our Saviour, and Lord Jesus Christ, which is our hope;

2 Timothy 1:1
PAUL, an apostle of Jesus Christ by the will of God, according to the promise of life which is in Christ Jesus,

Titus 1:1
PAUL, a servant of God, and an apostle of Jesus Christ, according to the faith of God's elect, and the acknowledging of the truth which is after godliness;

Philemon 1:1
PAUL, a prisoner of Jesus Christ, and Timothy our brother, unto Philemon our dearly beloved, and fellowlabourer,

...and then there is the book of Hebrews that does not include that salutation of Paul, that which is "the token in every epistle" he writes. 

The scriptures do not lie.  Either that token is in every epistle Paul wrote, or it isn't.  This is why Hebrews cannot be said to have been written by the Apostle Paul.