Molecular phylogenies contain information about the tempo and mode of species diversification through time. Because extinction leaves a characteristic signature in the shape of molecular phylogenetic trees, many studies have used data from extant taxa only to infer extinction rates. This is a promising approach for the large number of taxa for which extinction rates cannot be estimated from the fossil record. Here, I explore the consequences of violating a common assumption made by studies of extinction from phylogenetic data. I show that when diversification rates vary among lineages, simple estimators based on the birth-death process are unable to recover true extinction rates. This is problematic for phylogenetic trees with complete taxon sampling as well as for the simpler case of clades with known age and species richness. Given the ubiquity of variation in diversification rates among lineages and clades, these results suggest that extinction rates should not be estimated in the absence of fossil data.