Not only is a Carnal Mind focused on self but it is also limited to the Physical Realm. It has no understanding of the Spirit Realm and in many cases refuses to admit the existence of the Spirit Realm.
Enmity is the state or feeling of being actively opposed or hostile to someone or something.
So there is actually animosity toward God by those who reject the Spirit Realm. And that animosity is actually reciprocated by God to those who reject Him. That animosity is not agressive but passive in that He simply withholds Himself from them.
It will only be in The Judgment that the Wrath Of God is poured out upon the Carnal Minded.
As we interact with people in our lives we will encounter the Carnal Minded some of which have never heard the Gospel and some of which have heard it and rejected it.
Since without faith it is impossible to please God - and faith is a substance of the Spirit Realm - those who have rejected the Truth will not only have animosity toward God but will also have animosity toward you who love God. This is unavoidable.
Those who have a Love Of The Truth will desire God and He will reveal Himself to them In Christ Jesus. Those who have not a Love Of The Truth will be offended by the Truth and will stike out against it whenever it is expressed.