The simple answer to this question is that the church in the New Testament did not worship with instrumental music, and since we want to be like them, we do not worship with instrumental music.
Now, what does the New Testament say about worshipping God with music? In Ephesians 5:19 we read, “speaking to one another in psalms and hymns and spiritual songs, singing and making melody in your heart to the Lord.” In Colossians 3:16 we read, “Let the word of Christ dwell in you richly in all wisdom, teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord.”
These two passages teach us to sing by “speaking to one another” and “teaching and admonishing one another.” Instruments of music cannot speak, and they cannot teach and admonish. Now, if we do what God tells us to do, then we will sing and not play instruments.
We must submit ourselves to the righteousness of God which means respecting what Christ has said in His word. This is true for morality, salvation, church organization, and worship.