"For the flesh lusteth against the Spirit, and the Spirit against the flesh: and these are contrary the one to the other: so that ye cannot do the things that ye would" (Gal.5:17).
From the context we can see that Paul is speaking about a Christian's walk:
"This I say then, Walk in the Spirit, and ye shall not fulfil the lust of the flesh" (Gal.5:16).
When Paul contrasts walking in the Spirit with walking in the flesh he is speaking of living a God-centered life as opposed to living a self-centered life.
The following verse also speaks of the Christian's walk:
"So then they that are in the flesh cannot please God" (Ro.8:8).
A Christian can either walk after the Spirit or after the flesh:
"That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit" (Ro.8:4).
When Paul contrasts walking in the flesh with walking after the spirit he is speaking about being self-centered as opposed to being God-centered. Paul speaks about that same principle here:
"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" (Ro.8:5).
We can also understand that it is indeed possible for a Christian to walk or live after the flesh because Paul tells Christians that if they live after the flesh they shall die:
"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" (Ro.8:13).
If it is impossible that a Christian can walk after the flesh then it would make absolutely no sense for Paul to tell Christians that "if they live after the flesh you shall die."
The "death" spoken of here is in regard to the Christian's walk, that "we should also walk in newness of life" (Ro.6:4) so that "the life also of Jesus might be made manifest in our mortal flesh" (2 Cor.4:11). The second part of verse 13 is telling Christians that if they mortify the deeds of the body they will live. Christians are already received eternal life so Paul's words there are also referring to walking in newness of life.
From all of this we can understand that Christians can indeed walk in the flesh and when they live or walk that way they cannot please God. The Apostle John refers to that kind of walk as walking in darkness:
"This then is the message which we have heard of him, and declare unto you, that God is light, and in him is no darkness at all. If we say that we have fellowship with him, and walk in darkness, we lie, and do not the truth" (1 Jn.1:5-6).