Body mass index is calculated from two numbers and reported as though it described a person's body. It was constructed for a different purpose entirely, and most of the criticism it attracts follows from that mismatch.
It began as a population statistic
The formula came out of nineteenth-century work applying statistical methods to human characteristics, seeking a way to describe the average build of a population.
The objective was to summarise groups. Dividing weight by the square of height produced a figure that stayed roughly stable across adults of different heights, which made comparison between populations possible.
Nothing in that project involved assessing an individual's health, and the measure was not proposed for that.
The squared term is an approximation
Mass scales with volume, and volume scales with the cube of a linear dimension. A strictly geometric index would therefore use height cubed.
Human bodies do not scale geometrically as they get taller: proportions change. The square was chosen because it fitted observed data better than the cube did.
It is an empirical compromise, and it still tends to read high for tall people and low for short ones.
It cannot distinguish what the mass is made of
The calculation uses total body weight. Muscle, fat, bone and fluid all enter it identically, because the formula has no way to separate them.
A heavily muscled person and a sedentary person of the same height and weight produce the same number despite differing substantially in composition.
Fat distribution is invisible to it as well, though where fat sits is relevant to metabolic risk in ways that total mass is not.
Category thresholds are conventions
The cut-off values that divide categories were set by committee from population data, and they have been revised more than once.
Risk does not jump at a threshold; it changes gradually, so a person just above a line and one just below differ far less than the labels suggest.
The relationship between the index and health outcomes also varies between ancestral groups, which is why some countries use different thresholds.
Why it persists anyway
It survives because it is cheap, requires only a scale and a tape, and works reasonably well for the job it was built for: comparing groups and tracking trends over time.
Clinicians who need individual information add other measurements, such as waist circumference and blood markers, precisely because the index alone does not supply it.