Without the Spirit means without the Spirit. A believer is indwelt with the Spirit. An unbeliever does not have the Holy Spirit within.
For you to engage in desperate maneuvers in trying to insist that one without the Spirit is really a saved person --is demonstrating that you handle the Word of Truth deceitfully.
Without the Spirit does not have anything to do with quenching the Spirit. The individual in verse 14 never had the Spirit in the first place. Thus there can be no quenching since the Holy Spirit was never present in that person to begin with.
You are drifting away from the context and therefore the understanding of the verse.
What was Paul talking about?
He was speaking about understanding the Scriptures--illumination--understanding the "deep things of God." He begins talking about this in 1Cor.2:9,10, and even before that, but for our purposes we will start here:
1Co 2:9 But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him.
1Co 2:10 But God hath revealed them unto us by his Spirit: for the Spirit searcheth all things, yea,
the deep things of God.
God reveals the deep things of God by His Spirit to the spiritual Christian, not to the carnal Christian. The latter is unable to understand such truths.
1 Corinthians 2:11 For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God.
--Paul uses a comparison here. The first part of the comparison actually does speak of "the natural man," though it doesn't use that particular adjective.
IOW, only the man knows what thoughts he himself is thinking.
And, only the Spirit of God knows the deep things of God.
1 Corinthians 2:12 Now we have received, not the spirit of the world, but the spirit which is of God; that we might know the things that are freely given to us of God.
--Thankfully, compared to the rest of the world, God has given us "The Spirit which is of God," that we might know "the deep things of God," or those things which are freely given to us of God.
1 Corinthians 2:13 Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual.
--These are the things that Paul spoke--spiritual things; contrary to what the false teachers spoke--carnal things. They spoke spiritual truths, even "the deep things of God." They spoke the wisdom of men which also was carnality.
1 Corinthians 2:14 But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
--The natural man (of the flesh, carnal, lit. animal desires) does not receive the things of the Spirit of God (the deep things of the Spirit of God), neither can he know them, because he can't judge them.
He can understand the gospel, basic truths, but not the deep truths of God.
If what I say is not true, then all tract distribution, Bible distribution, and basic evangelism would be in vain. The natural man cannot understand it according to most Cals. But that is not what it is teaching. It is teaching that the "deep truths of God cannot be understood by "carnal minds," of the flesh, or of the world. IOW, they are not spiritual.
Therefore they are contrasted to those that are spiritual in verses 15 and 16, and those that do have the mind of Christ.
And in chapter 3 Paul addresses them as Carnal Christians because they are still immature in their standing before Christ, babes in Christ, still drinking the milk of God's Word, unable to proceed any further, as well as being outwardly carnal as is evidenced by the rest of the epistle.