But here's the problem. Christ loved the church and gave Himself for her (Eph. 5:25). Not the parachurch.
Christ is the Head of the church (Eph. 5:23), not of the parachurch.
He gave pastors and teachers for the equipping of saints for the work of service (Eph. 4:11).
The church is created for, founded upon, and united in, its allegiance to the person of Christ who exercises His headship through the specific truths of God's Word (Jn. 8:31-32; 17:17, 21, 23; Eph. 4:4-5). The task of enlisting and cultivating students of Christ has been entrusted to it (Matt. 28:18-20).
Let me rephrase that last thought as a question, and come at it from a different angle. Do you feel the need for instruction, for equipping for service? Do you see how much more there is to learn of Christ, of His person and work, of His will for your life? Are you boggled by the maze of differing and competing views, and longing for guidance and guarding amidst them? Christ already thought of all that, and more. He already made provision for those needs (Eph. 4:7ff.). The provision He made is men who are pastors and teachers, His personal ascension-gifts to His church.
So where do parachurch personnel come in? Well, that's the problem. Their leaders may or may not be (or be qualified to be) pastors.
Can anyone see a parachurch organization in the NT?