|Left: a depiction of an light-induced animated carbon-based molecule (retinal); which is similar to a human, also a light-induced animated carbon-based molecule, a CHNOPS+22 molecule specifically. Right (top): a carbon element tattoo on a human, oft-conceptualized as a form of "carbon-based life", who states: “I am a biochemist, studying to be a molecular biologist, the tattoo is carbon on the periodic table of elements. Since all living things on this planet at least are carbon based, from a chemical standpoint, it doesn’t get much more basic than carbon. Hence the tattoo.” –Erin(2008)|
The versatilities of the bonding geometries and dynamics of the carbon atom, with its four available valencies or bonding sites, is what gives carbon-based molecules the ability to be animated when exposed to light and various other reaction environments.
In 1934, Harold Blum, in his chemical peneplanation theory, discussed the possibility of ammonia (NH3) based life, in comparison to water (H2O) based life, seen on earth.
In 1950s, the term “carbon-based”, in contrast to silicon-based theories of life, began to appear in discussions of the possibility of life on Mars; the following begin one example:
“Our knowledge of physics, therefore, seems to tell us that living things anywhere in the universe must depend either upon carbon or upon silicon. Carbon-based life must be essentially similar to our own; there is no room for doubt upon that.”— Author (1955), “Article”, Science Digest (Ѻ), Vol 37
In 1967, people were citing Harold Morowitz per the assertion that “that if there is any life on Mars it is based on carbon. The chemical composition of the biosphere on Mars should be analogous to the terrestrial biosphere, though it may not be identical.” (Ѻ) The term ‘carbon-based life’, soon thereafter became a popular phrase in extraterrestrial life search circles, on the hypothesis that extraterrestrial life, if it exists, must be constructed primarily from carbon. 
The 19th century model of a human as a carbon-based organism, eventually was supplanted by the CHNOPS-based organism model; which is outlined below:
See main: Retinal molecule, Induced movementIn the absence of light, the carbon–carbon bond (red) at carbon 11 adopts a cis configuration and the chromophore adopts a bent structure (all of the other C=C bonds are trans). The two methyl groups (CH3, blue) at carbon atoms 9 and 13 point away from each other as indicated by the arrows. When exposed to light, retinal absorbs photons and the double bond at carbon 11 isomerizes from cis to trans and the now ‘all-trans’ retinal molecule straightens. This process also aligns the two CH3 groups, which now point in the same direction away from the main carbon chain. In vivo, the straightening of the retinal chromophore causes it to be released from the protein to which it is attached, because it no longer fits in the binding site. This, in turn, causes a change in the shape of the protein, which triggers a cascade that ultimately results in an electrical impulse being sent along the optic nerve, leading to visual perception. 
The following are related quotes:
“It is well known that carbon is required to make physicists.”— Robert Dicke (1961), “Dirac’s Cosmology and Mach’s Principle” 
1. Venter, J. Craig. (2006). What We Believe But Cannot Prove (pg. 21). Harper.
2. Liu, Zheng, Yanagi, Kazuhiro, Suenaga, Kazu, Kataura, Hiromichi, and Iijima, Sumio. (2007). “Imaging the Dynamic Behavior of Individual retianal Chromophores Confined inside Nanotubes” (figure 1), Nature nanotechnology, 2: 422-25.
3. Dicke, Robert H. (1961). “Dirac’s Cosmology and Mach’s Principle” (abs)(Ѻ), Nature, 192:440, Nov.
● Carbon-based life – Wikipedia.
● Carbon chauvinism – Wikipedia.
● Hypothetical types of biochemistry – Wikipedia.