Shouldn't the Gospels be part of the Old Testament?

Though you may not be pleased to hear it from us, your views of scripture are not accurate. In every case below, you have taken scripture out of context, distorting its true meaning and misapplied it to support your preconceived notion. You are interpreting the scriptures eisegetically, which always results in a false understanding. Instead, you must interpret each verse in its proper context so as to uncover the meaning the author intended, which is the proper form of interpretation called exegesis.

The conclusions you draw from your misinterpretations (i.e., that the four Gospels are not intended for Gentiles, etc.) are both bizarre and unbiblical. In fact, scripture itself contradicts your conclusion:

2Tim. 3:16 All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness; 
2Tim. 3:17 so that the man of God may be adequate, equipped for every good work. 

Furthermore, the entire Bible preaches the same Gospel of salvation through faith in a Messiah sent to Israel and to the whole world. Genesis preaches this Gospel. Exodus preaches this Gospel. The prophets preach this Gospel. And certainly, the first four books of the New Testament preach this same Gospel, as does Paul and the other epistles writers. The Gospel Paul mentions in 1 Corinthians 15 and elsewhere is the very same Gospel Jesus preached (it is His Gospel, after all), and it’s the same Gospel revealed progressively throughout the Old Testament (Genesis-Malachi).

As Hebrews declares:

Heb. 1:1  God, after He spoke long ago to the fathers in the prophets in many portions and in many ways, 
Heb. 1:2 in these last days has spoken to us in His Son, whom He appointed heir of all things, through whom also He made the world. 

There is no “Old Testament” Gospel. Yes, many in Israel and many among the Gentile nations have neglected the true Gospel and have pursued a false salvation of works, but the Bible is not to blame for that mistake. Neither the Old Testament nor the New Testament told Jews or Gentiles to pursue God through works. The Bible has preached the same Gospel from Genesis to Revelation, but many refuse to hear it. 

Only by faith in the promises of God may one be saved, and this is the way Abraham was saved in the Old Testament (prior to Christ), and it is also the way we are saved now. As Paul said:

Rom. 4:3 For what does the Scripture say? “Abraham believed God, and it was credited to him as righteousness.” 
Rom. 4:4 Now to the one who works, his wage is not credited as a favor, but as what is due. 
Rom. 4:5 But to the one who does not work, but believes in Him who justifies the ungodly, his faith is credited as righteousness, 

Finally, it might help your understanding to remember that all New Testament scripture (including the Gospel accounts) were written long after Jesus’ death. So, therefore, all New Testament scripture was written after the Law had been completed by Jesus’ death and resurrection.
 

Scripture quotations taken from the (NASB®) New American Standard Bible®, Copyright © 1995, 2020 by The Lockman Foundation. Used by permission. All rights reserved. www.lockman.org