This area confuses some people. If you don't understand the various reasons for speaking in tongues, then Scripture itself can and will be used out of context in an attempt to prevent its use.
You are failing to understand the overall argument and then the immediate argument in chapter 14.
1. Chapter 12 - Spiritual gifts are not determined by your desires or choice but by God, His will, His placement and purpose and He does not purpose for all Christians to receive all gifts.
2. Chapter 13 - Spiritual gifts are to be exercised according to the principles of love because love is superior and eternal and gifts are not.
3. Chapter 14 - Spiritual gifts used according to love seek the edification of all (vv. 1-17) but God never designed tongues to be used in the church but on the mission field as a sign to Israel (vv. 18-21) according to the scriptures. Their use in the congregation is not prohibited but restricted within the principles of edification (order and descency and propriety).
Between the events on the day of Pentecost and Saint Paul's teaching to the Corinthian church, there are different purposes for tongues:
Evidence of the indwelling Holy Spirit (Acts 2:1-4 Acts 10:45-46 Acts 19:1-6)
Therefore you are denying salvation to anyone who does not speak in tongues for all who are not indwelt in the Spirit are lost - Rom. 8:7-9.
Neither is it a sign to unbelievers but UNBELIEVING JEWS - 1 Cor. 14:20-21
There are unlearned unbelievers (gentiles) who think you are crazy but to learned unbelievers (Jews that are learned in scriptures) it is the sign to them that their Christ has come (Isa. 28:12-15 with 1 Cor. 14:20-21.
A ministry of the Holy Spirit to express worship...to magnify and extol God (Acts 2:8-11 Acts 10:45-46)
In neither case was it for worship. In Acts 2:8-11 it was to confirm Jesus as the Christ TO ISRAEL. In Acts 10:45-46 it was to confirm TO JEWS (Peter and the six other Jews) that God had accepted them and thus fit for baptism and membership in an all Jewish congregation.
A public ministry gift used to communicate a message from God through an interpreter "when ye come together"--or the public gathering of the church (1 Cor. 14:26-28)
It is listed with the prophets (not merely prophesying) as used as a revelatory gift as they had no scriptures for Church policy and practice or doctrine.
Praying in tongues--or praying with the Spirit used in intercessory prayer (1 Cor. 14:14-17)
There is not even a hint of "intercessary prayer" in these verses. Paul is putting forth his own example concerning his REFUSAL to pray or sing or speak in tongues when his mind cannot be edified by it. He is rebuking any use of tongues that does not edify both the speaker and the hearer.
He is not comparing the two here, he is comparing "praying in the spirit"(tongues) to praying with understanding (with your mind).
No he is not! You are perverting the plain sense of these scriptures. He is condemning any use of tongues that does not edify both the speaker and hearer. To suggest his "inner man" is built up distinct and separate from his mind is absurdly rediculous and completely occultic.
It does not say that the one praying in the spirit is not being edified. Because vs. 17 says that He gives thanks well. The others are not edified without the interpretation.
You are failing to completely to understand his line of argument. He already determined in regard to HIMSELF that "I WILL NOT" utter tongues without his mind participating. Neither will he simply edify himself with conscious understanding of what he is saying without sharing it when others are present regardless how he uses it (pray, sing, preach, teach, prophesy, etc.).
16 Else when thou shalt bless with the spirit, how shall he that occupieth the room of the unlearned say Amen at thy giving of thanks, seeing he understandeth not what thou sayest?
If I pray with understanding as I determined above but don't give understanding to the hearers I am edified but I fail to seek the edification of the listeners:
17 For thou verily givest thanks well, but the other is not edified.
You added your own conclusion about it not edifying the one praying in the spirit! THe Bible does not say that!
It most certainly does if you simply follow his argument from verse 13. He is refering to HIS OWN PERSONAL use of tongues in verses 13-16. He is determined NEVER to speak in tongues unless his own mind is edified and NEVER simply for self-edification when others are present as that violates the principles of edification for the use of gifts according to the way of love (v. 17).
You clearly do not understand the clear teaching of Paul but simply insert what you want where you want it.