The wetting behavior of homopolymer on a chemically identical polymer brush is mathematically equivalent to the interaction between a pair of opposing brushes in a matrix of parent homopolymer. We examine both systems using self-consistent field theory (SCFT) with a new highly efficient and accurate algorithm. Our calculations provide compelling evidence that the global minimum in the free energy curve remains at a finite film thickness, implying that the brush/homopolymer interfacial tension, gamma (b/h), is always positive favoring dewetting, or equivalently that an attraction always exists between opposing brushes. Nevertheless, we identify a region at low homopolymer molecular weights where gamma (b/h) is negligible, in which case complete wetting is highly metastable and the attraction between opposing brushes is extraordinarily weak. Furthermore, we demonstrate that SCFT is in good quantitative agreement with experiment. In contrast, we find that earlier predictions based on strong-stretching theory are terribly inaccurate.