Percolation is ubiquitous. The long accepted concept for such processes is that they undergo a continuous transition, including the explosive percolation under intensive discussions. However, the violent spreading of historical co-epidemics has suggested a new type of percolation transition. In our recent work, we proposed a model involving cooperation between different species of pathogens (agents). Here, a fundamentally different scenario from classic ordinary percolation was unveiled, showing that both continuous and discontinuous phase transitions are possible to arise. Our Monte Carlo simulations suggest a critical role of the size distribution of loops in the underlying topology in determining the order of phase transition. A first-order transition is clearly imminent when there is a barrier established by the loops, which draws a close relation to nucleation. In such cases, an epidemic either dies out prematurely or goes for cascaded mutual infections right at a threshold. The model suggests a cooperation-induced instability on complex networks, which can also underpin binary chemical deposition or failure spreading phenomena.