Posting this because although this information is focused on Native American languages, this also applies to the Greenberg Language Phylums of African languages by consequence since the same methods were used.
"Whereas Greenberg’s classification has been widely and uncritically used by human geneticists, it has been rejected by virtually all historical linguists who study Native American languages. There are many errors in the data on which his classification is based (Goddard 1987; Adelaar 1989; Berman 1992; Kimball 1992; Poser 1992), and Greenberg’s criteria for determining linguistic relationships are widely regarded as invalid. His method of multilateral comparison assembled only superficial similarities between languages, and Greenberg did not distinguish similarities due to common ancestry (i.e., homology) from those due to other factors (which other linguists do). Linguistic similarities can also be due to factors such as chance, borrowing from neighboring languages, and onomatopoeia, so proposals of remote linguistic relationships are only plausible when these other possible explanations have been eliminated (Matisoff 1990; Mithun 1990; Goddard and Campbell 1994; Campbell 1997; Ringe 2000). Greenberg made no attempt to eliminate such explanations, and the putative long-range similarities he amassed appear to be mostly chance resemblances and the result of misanalysis—he compared many languages simultaneously (which increases the probability of finding chance resemblances), examined arbitrary segments of words, equated words with very different meanings (e.g., excrement, night, and grass), failed to analyze the structure of some words and falsely analyzed that of others, neglected regular sound correspondences between languages, and misinterpreted well-established findings (Chafe 1987; Bright 1988; Campbell 1988, 1997; Golla 1988; Goddard 1990; Rankin 1992; McMahon and McMahon 1995; Nichols and Peterson 1996).
Consequently, empirical studies have shown that “the method of multilateral comparison fails every test; its results are utterly unreliable. Multilateral comparison is worse than useless: it is positively misleading, since the patterns of ‘evidence’ that it adduces in support of proposed linguistic relationships are in many cases mathematically indistinguishable from random patterns of chance resemblances” (Ringe 1994, p. 28; cf. Ringe 2002). Because of these problems, Greenberg’s methodology has proven incapable of distinguishing plausible proposals of linguistic relationships from implausible ones, such as Finnish-Amerind (Campbell 1988). Thus, specialists in Native American linguistics insist that Greenberg’s methodology was so flawed that it completely invalidates his conclusions about the unity of Amerind, and Greenberg himself estimated that 80%–90% of linguists agreed with this assessment (Lewin 1988).
Given this, the use of Greenberg’s (1987) classification can confound attempts to understand the relationship between genetic and linguistic variation in the Americas. Many studies of Native American genetic variation continue to use this classification (e.g., Bortolini et al. 2002, 2003; Fernandez-Cobo et al. 2002; Lell et al. 2002; Gomez-Casado et al. 2003; Zegura et al. 2004). However, Hunley and Long (2004) recently showed that there is a poor fit between Greenberg’s classification and the patterns of Native American mtDNA variation. On the basis of their findings, we believe that Greenberg’s groupings should no longer be used in analyses of mtDNA variation."