I doubt this is correct. Women tend to be mezzos and men tend to be baritones entirely based on the structure of their vocal apparatus, not because they are trying to force a sound (with the possible exception of gay men). In most cases, men who are good singers tend to sing high because that is where the demand is (tenors in classical music and also very high pop music), but as they learn to relax their larynx their comfortable range often drops.