We are not debtors to the flesh
Therefore, brethren, we are debtors, not to the flesh to live after the flesh. For if ye live after the flesh, ye shall die: but if ye through the Spirit do mortify the deeds of the body, ye shall live. Rom. 8:12-13
When someone does something good to us, we will often say that we owe them a debt of gratitude. However, what the apostle is saying here is that the believer should have no such attitude of gratitude towards the flesh, the flesh being our nature in opposition to God. For what does the flesh do? To be carnally minded is death (6). It is to be hostile to God (7), and in a state in which we cannot please God (8). It is the opposite of being in the Spirit. There is nothing desirable or praiseworthy that the flesh can do for us.
Rather, we are to put the "deeds of the body" - the flesh - to death. How do we do this? We do it, not by our own strength, but in the strength which God provides, "through the Spirit." Note the balance: there is no "let go and let God" theology here, for we are the ones who must mortify and put to death the deeds of the body. But it is through the Spirit, for without God's grace we can do nothing (Jn. 15:5). As John Piper puts it, we act the miracle. So we fight sin with all our might while simultaneously relying on the strength of grace. We work out our own salvation because it is God who works in us both to will and to do of God's good pleasure (Phil. 2:12-13).
We do so because nothing less than life is at stake: "for if ye live after the flesh ye shall die." As John Owen has famously written, "Be killing sin, or it will be killing you." All sin can give us in the end is death (Rom. 6:23), physical and spiritual and eternal. But through Christ and the Spirit who mediates his presence we are enabled by God's grace to put to death the deeds of the body. Indeed, all who belong to him will do so, "for as many as are led by the Spirit of God, they are the sons of God" (Rom. 8:14).
Let us therefore refuse to believe the lie that sin so often whispers in our ear, that we cannot conquer the sin which does so easily beset us (Heb. 12:1). Rather, let us lay it aside, because we are not waging war on sin in our own strength but in the strength which God provides. Indeed, we are more than conquerors through him that loves us (Rom. 8:37). Praise God for his amazing and empowering and sin-killing grace!