In the grand schema of evolution, a mythical prokaryote to eukaryote cellular transition allegedly gave rise to the diversity of eukaryotic life (eukaryogenesis). One of the key problems with this idea is the fact that the prokaryotic world itself is divided into two apparent domains (bacteria and archaea) and eukarya share similarities to both domains of prokaryotes while also exhibiting many major innovative features found in neither. In this article, we briefly review the current landscape of the controversy and show how the key molecular features surrounding DNA replication, transcription, and translation are fundamentally distinct in eukarya despite superficial similarities to prokaryotes, particularly archaea. These selected discontinuous molecular chasms highlight the impossibility for eukarya having evolved from archaea. In a separate paper, we will address alleged similarities between eukarya and bacteria.