William May explains why quality-of-life assessments are inappropriate for determining who should live and who should die in his book Catholic Bioethics and the Gift of Human Life:
"Quality of Life" judgments are inescapably arbitrary and unjust. Different authors assign different qualities that one needs to possess "meaningful" life, and the same authors at times list different qualities in different apologias for their position. More significantly, the qualities alleged to make life worthwhile (intelligence, ability to respond to stimuli, awareness of others, etc.) all admit of enormous differences in degree. But some cutoff point has to be assigned, above which the quality of life is "meaningful" and below which it is not so that death can be mercifully administered. Such cutoff points are arbitrarily asserted, with different authors assigning different "weight" to different factors and different degrees of ability within the chosen criteria. It is evident that this way of determining who should live and who should die is utterly arbitrary and unjust."
It is an evil arrogance that allows an individual to presume his assessment of the worthiness of another's life is more valid than this other individual's own assement of the meaningfulness of his own life.