Current technologies for converting biomass to fuel products are severely hindered by cellulose recalcitrance. Recently, it was found that certain classes of ionic liquids (ILs) can dissolve cellulose into its constituent glucan chains. To understand the molecular forces provided by ILs to break down crystalline cellulose, we performed all-atom molecular dynamics (MD) simulations of two extreme states of cellulose: a crystalline microfibril and a dissociated state in which all the glucan chains of the crystalline microfibril are fully detached from each other. MD simulations of the two states are performed in water and in the IL 1-butyl-3-methylimidazolium chloride (BmimCl) to provide a comprehensive analysis of solvent effects on cellulose dissolution. The results highlight two unprecedented insights in the dissolution of cellulose by solvent-mediated interactions. First, the perturbation of solvent structures by dissolved glucan chains can be a dominant factor in determining solubility. We show that the insolubility of cellulose in water at 300 K arises mostly from reduction in solvent entropy. Second, for BmimCl, the driving force for cellulose dissolution comes from energetics, and more importantly, that both the Cl- and the Bmim+ ions can exert disruptive effects on C-H--O intersheet interactions, which we show to be the most significant molecular source of cellulose recalcitrance. Cl- anions are observed to form hydrogen bonds (HBs) with the hydroxyl groups of glucan chains from either the equatorial or axial directions, thereby disrupting intersheet connections. Bmim+ cations are observed directly interacting with glucan chains along the axial directions. Therefore, the ability of BmimCl to interact favorably with not just the OH groups of cellulose, but also the CH groups of cellulose is what enables it to disrupt the entirety of cellulose's internal interaction network and makes it an effective cellulose solvent.