Superficially, the archaea resemble bacteria, and until the 1990s everyone thought they were bacteria. Then Carl Woese sought to describe the ‘true’ evolutionary history of life. He chose a biological molecule that is so critical for life that every organism must have it. He then hoped to be able to trace changes in this molecule throughout all organisms and so to discover the pattern of change as living creatures evolved. The molecule he chose was the RNA component of the small subunit of the ribosome. Ribosomes are the molecular machines that splice together proteins based on information in the DNA. (Spoiler alert: Carl Woese’s system did not work as he hoped for tracing evolutionary relationships. See HGT)
Until Carl Woese compared ribosomal RNAs in various organisms, nobody suspected that some prokaryotic cells were quite different from the majority of such cells (i.e. the bacteria; see prokaryotes). On the basis of a major difference in the DNA sequence for ribosomal RNA molecules, he declared that the new group (which he named archaea) must have diverged a very long time ago from the bacteria, assuming that they had both come from a common ancestor.
Archaea look much like bacteria in their tiny size, unicellular condition, and their circular chromosome (not bounded by a nucleus) inside the cell. However, many of the archaea live in very hostile environments such as those with high temperatures, high salinity, high levels of heavy metals etc.
Scientists like to carry out chemical comparisons between the bacteria, archaea and the eukaryotes because they are looking for clues as to which group was ancestral to another (based on the assumption that they evolved rather than that they were created). According to Ford Doolittle, all archaea use diphytanylglycerol diether or dibiphytanylglycerol tetraether or both as major lipid constituents. However, bacteria and eukaryotes use diacylglycerol-derived lipids. Moreover, bacterial cell walls are composed of peptidoglycan which are never found in archaea and eukaryotes. [W. Ford Doolittle. June 25, 1999. Phylogenetic Classification and the Universal Tree. Science vol. 284 pp. 2124-2128. p. 2125]
Some features of eukaryotes are more like archaea and others are more like bacteria. The creator did not have to choose to confer one set of characteristics exclusively on one group or the other! Eukaryotes use tubulin and actin-based cystoskeletons to give structure to their large cells. There are no such features in either bacteria or archaea. While the replication, transcription and translation related proteins in archaea are similar to those in eukaryotes, “many, (perhaps most) enzymes involved in eukaryotic cytosolic metabolism are of bacterial origin, not of archaeal as one would expect.” [Doolittle p. 2126] Dr. Doolittle therefore criticized the trend in interpretation at that time (and still evident today), to attribute eukaryotic origins to the archaea. Thus, he declared: “One must ask why archaea are still considered to be eukaryotes closest relatives, when only a minority of eukaryotic genes may show this to be true.” [p. 2126]
It is apparent that there is no obvious connection between these groups of organisms. The relationship that one chooses to promote will depend upon which features one wants to emphasize, leading to highly subjective conclusions. The identification of the archaea is an added complication for people trying to propose an evolutionary origin for life. There is absolutely no reason why one would not simply instead choose to focus on the work of God, the Creator.