1. Question Restatement
What is Paul's reasoning to say it is possible to fall from Grace, by obeying the law?
2. Answer :
There is a very, very, important "qualification" that clarifies this:
NASB, Galatians 5:4 - You have been severed from Christ, you who are seeking to be justified by law; you have fallen from grace.
When Paul states that he is "being all things to all people", (1 Corinthians 9:19-23), by obeying the law, (or not) - he is NOT doing this for the purpose of "being justified by the law".
As long as he wasn't doing this, (in his heart), he submitted to the law, (or didn't), in order to be a "Minister of Reconciliation", (2 Corinthians 5:12).
This has nothing to do, at all, with someone obeying the commandments of Jesus - as a demonstration of "Love", and proving a covenant relationship already there.
"Justification by the Spirit" Definition: Under Christ, in order to be judged "moral", that one walks "justly": Christians live under the law of mercy and favor by forfeiting the right to accuse, (which is granted under laws that condemn). Christians forgive unconditionally because it is the only "just response" to having been forgiven unconditionally, (this is walking in the ministry of reconciliation and forgiveness). Because of this, Christians might naturally obey the commandments of Jesus. Judgment will be merciless to those who do not show mercy, (James 2:13).
3. Explanation - Consistent Theology Regarding Favor and Mercy
Seeking to be "Right and Moral before God" by complying with "divine morality", is not trusting in a promise. By relying on "the law" for "spiritual intimacy", or "morality/justification" - is a rejection of relying on Jesus' unconditional advocacy on the Cross, not trusting that Jesus' advocacy is completely sufficient for justification.
Paul uses Scripture as the premise that Christians can be severed from Christ, if one chooses to live under law, rather than trust:
NASB, Galatians 4:23 - But the son by the bondwoman was born according to the flesh, and the son by the free woman through the promise. 24 This is allegorically speaking, for these women are two covenants: one proceeding from Mount Sinai bearing children who are to be slaves; she is Hagar. 25 Now this Hagar is Mount Sinai in Arabia and corresponds to the present Jerusalem, for she is in slavery with her children. 26 But the Jerusalem above is free; she is our mother.
The Two Laws are Anti-Thetical towards each other:
NASB, Galatians 5:17 - For the flesh sets its desire against the Spirit, and the Spirit against the flesh; for these are in opposition to one another, so that you may not do the things that you please. 18 But if you are led by the Spirit, you are not under the Law.
Paraphrase: But you, who are under the law of the Spirit, are not under law [the condemns] - and therefore forfeit any right under that law, not under its obligations. You cannot appeal to a judge that you are dead to a law, to escape judgment, and then assert a right to accuse under that same law that you claimed you are dead to.
2 Corinthians 5:16-20 - Therefore from now on we recognize no one according to the flesh; ... 17 Therefore if anyone is in Christ, he is a new creature; the old things passed away; ... 18 Now all these things are from God, who reconciled us to Himself through Christ and gave us the ministry of reconciliation, 19 namely, that God was in Christ reconciling the world to Himself, not counting their trespasses against them, and He has committed to us the word of reconciliation.
Conclusion: Seeking to be justified by the law, by definition, is a fear that God WILL count trespasses against you, regardless of what Jesus did on the cross. This is in effect, "Being severed from Christ" - since one judges Jesus' unconditional advocacy for the world as insufficient.