Short-lived comets are replenished from the Kuiper Belt. Because Kepler's Laws permit us to know the entire orbit of a comet if we observe it moving near the Sun, scientists inferred the existence of a large collection of icy rocky objects out beyond Pluto.
Late on, the existence of the Kuiper Belt was confirmed by observation of some of the larger objects in it.
Due to their small size and extreme distance from Earth, the chemical makeup of KBOs is very difficult to determine. The principal method by which astronomers determine the composition of a celestial object is spectroscopy. When an object's light is broken into its component colors, an image akin to a rainbow is formed. This image is called a spectrum. Different substances absorb light at different wavelengths, and when the spectrum for a specific object is unravelled, dark lines (called absorption lines) appear where the substances within it have absorbed that particular wavelength of light. Every element or compound has its own unique spectroscopic signature, and by reading an object's full spectral "fingerprint", astronomers can determine its composition. Analysis indicates that Kuiper belt objects are composed of a mixture of rock and a variety of ices such as water, methane, and ammonia.
Kuiper belt - Wikipedia
"Answers in Genesis" merely denied what has been observed about the composition of these bodies. It was the only way they could maintain their claim about short-lived comets.