Paul is talking about his own self — the "I" that wants to do good but keeps failing — and in doing so he's pointing to a self that, apart from God, is fundamentally incomplete and unable to deliver on its own best intentions.

In this verse, "that" points specifically to the flesh as the problem — not the whole person, not the soul, not the new nature, but this one particular part of you that remains uncooperative with what you genuinely want to do.

Your fallen human nature — the part of you that wants to do right but keeps failing — is not your whole self, just the broken piece you're stuck wrestling with.

Paul is being brutally honest that within himself — his human, fleshly self — there is simply nothing good to be found.

Paul recognizes that wanting to do right comes naturally to him, but good intentions alone have no power to produce good actions.

The desire to do right is always within reach, but so is the pull toward wrong — both are close, both are accessible, and which one you act on is the daily tension Paul is describing.

Even when Paul desperately wants to follow through on doing good, he finds he lacks the power to actually carry it to completion on his own.

In this verse, Paul is confessing that his natural self contains nothing truly worthwhile or morally excellent — the kind of genuine goodness that actually meets God's standard, not just good intentions.

Paul isn't saying he can't locate good actions the way you'd search for lost keys — he's saying that no matter how hard he looks within himself, there's simply nothing there capable of following through on what he knows is right.