Archaeplastida (=Kingdom Plantae) are primary plastid-bearing organisms that evolved via the endosymbiotic association of a heterotrophic eukaryote host cell and a cyanobacterial endosymbiont approximately 1,400 Ma. Here, we present analyses of cyanobacterial and plastid genomes that show strongly conflicting phylogenies based on 75 plastid (or nuclear plastid-targeted) protein-coding genes and their direct translations to proteins. The conflict between genes and proteins is largely robust to the use of sophisticated data- and tree-heterogeneous composition models. However, by using nucleotide ambiguity codes to eliminate synonymous substitutions due to codon-degeneracy, we identify a composition bias, and dependent codon-usage bias, resulting from synonymous substitutions at all third codon positions and first codon positions of leucine and arginine, as the main cause for the conflicting phylogenetic signals. We argue that the protein-coding gene data analyses are likely misleading due to artifacts induced by convergent composition biases at first codon positions of leucine and arginine and at all third codon positions. Our analyses corroborate previous studies based on gene sequence analysis that suggest Cyanobacteria evolved by the early paraphyletic splitting of Gloeobacter and a specific Synechococcus strain (JA33Ab), with all other remaining cyanobacterial groups, including both unicellular and filamentous species, forming the sister-group to the Archaeplastida lineage. In addition, our analyses using better-fitting models suggest (but without statistically strong support) an early divergence of Glaucophyta within Archaeplastida, with the Rhodophyta (red algae), and Viridiplantae (green algae and land plants) forming a separate lineage.