Its the consequence of assuming no change in supply and assuming that there are other competing goods (e.g., food) which will compete for the marginal dollars for the same population of buyers (and hence that demand is not perfectly inelastic.)
Engel's law (the food example) doesn't really impact it that much because the income elasticity of food is between 0 and 1. By your logic nothing has an income elasticity of demand greater than 1 because of competing with food.
