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Living things are composed of cells and undergo metabolic processes. Candle wax is composed of a mixture of carbon compounds that may have come from formerly living things (but is incapable of metabolic activity). That's why both living things and petroleum based products are carbon-based (sometimes referred to as organic).
The question was probably asked to see if you understand the distinction between organic (carbon-based) materials and living things. All living things are carbon-based, but not all carbon-based things are living.
The question is also checking to see if you realize that a burning flame undergoes the same basic chemical reaction as cellular respiration (i.e., combustion). In the cells of living things, glucose is broken down in the presence of oxygen to produce carbon dioxide and water. In a non-living candle, wax (which is also a carbon-based fuel like glucose) is also broken down in the presence of oxygen to produce carbon dioxide and water. So you see, just because a non-lving thing undergoes the same type of chemical reaction doesn't prove that it is living.
A very quick test of living vs. non-living is to determine if the "organism" is capable of reproducing itself. I've never seen baby candles.
Kind of depends on how you look at it; in terms of "propagation", one could argue that sparks from a flame "propagate" the flame and create new flames.
However, the key characteristic of true propagation is the ability to transfer one's innate characteristics to one's offspring. The flame's characteristics are a function of the fuel and the oxidizer and not of the flame itself.
As an example, a wood or match flame can propagate to a gas flame, but the characteristics of a gas flame are unique to the natural gas and the oxygen in the air. The gas flame can propagate to a liquid flame, such as with alcohol or gasoline. Again the characteristics change as a function of the materials at hand and not the flame itself.
Moreover, a flame has no purpose, other than to consume all its avaibable fuel. There is no mechanism to conserve itself so that it can propagate elsewhere. Contrast this with the classic virus, which is mostly pure genetic material encapsulated by a protein shell. Viruses can lay dormant for years, waiting for right conditions to co-opt the host organism to propagate copies of itself. Because the virus does not perform maintenance, there is great debate about whether viruses are alive.