Why do economists pay little attention to the algebraic sign of the elasticity of demand for a good with respect to its own price, yet pay careful attention to the algebraic sign of the elasticity of demand for a good with respect to another good's price?

As long as demand curves slope downwards, the price elasticity of demand will always be negative. Thus, for the sake of convenience, with a downward sloping demand curve, the algebraic sign of the elasticity of demand for a good with respect to its own price can be neglected.

However, the algebraic sign does matter very much when investigating the cross-price elasticity of demand (i. e. the elasticity of demand for a good with respect to another good's price). When the elasticity of demand for one good with respect to the price of another good is positive, the two goods are substitutes, when this cross-price elasticity of demand is negative, the two goods are complements.