The arguments for Feature Geometry are set forth in Clements' 1985 paper 'The Geometry of Phonological Features'. By way of conceptual background, the question of how/whether features are organized was current in much work in autosegmental phonology, once it was realized that in principle every feature could exhibit "autosegmental autonomy". A simple model (the 'bottlebrush model') had been contemplated, that all features link directly to the CV core. For the CV tier itself, see Clements & Keyser CV phonology and references therein. The problem is that features often act as a class, hence we find "place assimilation" rules in languages. The formal theory did not treat simultaneous assimilation of [anterior, coronal, back, distributed] as any different from simultaneous assimilation of [anterior, voice, continuant, lateral], but while the former is well-known, the latter is completely unattested. The theory also makes it more complicated to perform total assimilation of place in a language that has many place contrasts (such as Malayalam) and simpler to write a rule that only partially (and depending on formulation, bizarrely) assimilates place features. The defects were identified in an unpublished paper by Mohanan ('The structure of the melody'), who identifies the fact that features group together functionally, and proposes the essential concept of "class node" which he calls "feature block".
Clements expands and refines on this in the 1985 paper, assembling a set of "functional unity" instances, for instance preaspiration in Icelandic, Klamath nasal-lateralization and debuccalization. By way of important prior results leading to the theory, it had been previously established in many papers that partially and fully assimilated consonant clusters exhibit a kind of special phonological integrity labeled integrity and inalterability, and there was a structural proposal (about crossing lines) which required having "an association line" between e.g. m and p in mp, whereby an epenthetic vowel could not cross that line (thus /mp/ does not become [mip] via a general cluster-busting epenthesis rule). Feature Geometry thus provided the last logical stop in deriving the integrity / inalterability facts.