Living in the flesh is what it says
You are serving self. (The flesh)
A babe in christ still serves self. He or she has to learn to love as God loved them. Thats why they can only be fed milk..
but they are just as saved as the man of Christ who is mature in all ways..
Rather, Scripture gives specific definitions of being in flesh and in s(S)pirit.
Romans 8:5-11 KJV
5) For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit.
6) For to be carnally minded is death; but to be spiritually minded is life and peace.
7) Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.
8) So then they that are in the flesh cannot please God.
9)
But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his.
10) And if Christ be in you, the body is dead because of sin; but the Spirit is life because of righteousness.
11) But if the Spirit of him that raised up Jesus from the dead dwell in you, he that raised up Christ from the dead shall also quicken your mortal bodies by his Spirit that dwelleth in you.
Simply stated, you are not "in flesh" if you are indwelt by the Holy Spirit.
There is a lot more that can be said of course, which we can look at the various passages. We are in flesh, until we are reborn, at which time we are in the Spirit. I believe this refers to the source of our living. Prior to rebirth, we derived our "being alive" because we inhabited living bodies. Now, in Christ, we derive our "being alive" from God's spirit, a different sort of life.
Paul actually uses the language a couple of ways. Here, he is describing our source of life, and how this source survives our flesh death, even overcoming it. While in his letter to Corinth he speaks of being in flesh, but not warring after flesh. Just because we still live in these bodies, our battle isn't fought the way this body fights.
Much love!