One key aspect of scripture is the continual distinction between Israel and the church.
Consider Romans 11:25:
“For I do not desire, brethren, that you should be ignorant of this mystery, lest you should be wise in your own opinion, that blindness in part has happened to Israel until the fullness of the Gentiles has come in.” [1]
Blindness has happened to Israel until. The church has not replaced Israel in God’s program for the ages. Israel has, at a national level, been set aside until the fullness of the Gentiles are brought in. Once that is accomplished, God will once again work with Israel, until “all Israel will be saved” (Romans 11:26 [1]).
The scriptures are replete with this idea of a distinction between Israel and the church. Consider the following passage from Ephesians 2:14-17:
“For He Himself is our peace, who has made both one, and has broken down the middle wall of separation, having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace, and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity. And He came and preached peace to you who were afar off and to those who were near.” [1]
The church has not replaced Israel, assuming the promises given the nation in some spiritual sense. Rather, God has brought Jews and Gentiles together into something brand new, that did not exist in the Old Testament. There is no need for Him to preach to those who are near if they’re either already part of the body or being replaced. It is clear that this new “one body” came into existence only after the cross, so it cannot include the nation of Israel in the Old Testament. This precludes the church joining and shouldering out Israel.
In Colossians 1:27 there is a distinct feature of the church:
“To them God willed to make known what are the riches of the glory of this mystery among the Gentiles: which is Christ in you, the hope of glory.” [1]
The church has a unique characteristic that was not present in the Old Testament, namely “Christ in you”. No other group in all history has this truth as the church does now. It may be that no group in the future will have this unique characteristic either.
This small sampling of scripture is far too brief to fully explain the distinction between Israel and the church. However, one key tenant of dispensationalism is the distinction, and therefore dispensational teaching also well describes the the scriptures in this aspect.
[1] New King James Version, 1982, Thomas Nelson, Inc.