By definition an enemy is one whom we view as threatening in some sense, perhaps in simply wishing us ill fortune. We also encounter the idea of mutual enemies, which suggests, that in some cases, one person may view another as an enemy, while the second party does not, in turn, view the first in the same way. In such cases, what happens when the second party learns that he is considered an enemy? Does the second party then come to see the first party as an enemy? Is someone who considers me an enemy automatically my enemy?
In the NT, the word translated "enemy" incorporates the idea of hatred, the very opposite of "agape" according to Vine's. Incongruously, Jesus instructs us to love our enemy, the one who hates us. We are not to become mutual enemies, apparently.
Interestingly, in order for God to view man as an enemy, He would have to hate man. By no stretch could we conceive that God views man as a threat, rival, or assailant. Therefore if God considers man to be His enemy, then it must be because He loathes and detests humanity. One could, however, easily imagine that man views God as an enemy, since, in accordance with prevailing religious thought, God does actually threaten man in a multitude of ways, including eternally in torment. If by enemies, we don't mean the mutual variety, then the state of hostility which supposedly exists between God and man is readily conceived and explained as man's doing and not God's.
How can the God defined as love, be my enemy, one who hates and threatens me. It is inconceivably illogical. If I exist in a state of enmity with God, it has to be my hatred which is at fault. Who or what do I hate and why? Who has persuaded me make the God of love my enemy? When I learn to love my enemy, maybe I'll learn to love God and myself in the process. It would be a nice step forward in applying the Golden Rule if the way I view God and myself were elevated above the picture projected by religious tradition.
If one goes to the dictionary, we encounter words which are synonymous with or closely related to the word enemy: Foe, ill-wisher, attacker, combatant, competitor, rival, emulator. These related words raise the broader idea that an enemy can be one with whom we engage in competition. This corresponds to the common use of the word enemy to identify rivals in business or sporting events. Enemies in this sense don't necessarily inspire hatred but they do strive in opposite directions as having different goals. To the extent that God and man strive in different directions, they could be considered enemies in this sense.
The church's preoccupation with opposing enemies, human and otherwise, is a total refutation of the Christian principles of peace, love, self sacrifice, joy, humility, and meekness. All the church's preoccupation with external enemies does is divert attention from the simple minded incongruity of its doctrine and message. Quoting scripture and insisting on thousand year old theologies does not mitigate the obvious disconnect one iota.