Reportedly, the vocalist on “Obsession” is portraying the role of a stalker. And the lady whom he is stalking, i.e. the addressee, is his “obsession”. And yes, the singer does come off as being quite creepy...
This song is based on the singer (Pat Benatar) acknowledging that “love is a battlefield”. Or perhaps a simpler way of looking at this statement is that she understands that there is a very-strong potential...