The coelacanth, thought extinct for ages, is still living

[edit] Claim

The coelacanth, thought to have been extinct for 70 million years and used as an index fossil for earlier ages, was found still to be alive.

A Coelacanth is not a species of fish as this claim implies: "Coelacanth," named after a genus, Coelacanthus, that lived from the Permian until the Jurassic, is an order level grouping of creatures with both ancient and modern representatives that are morphologically distinct from each other.
Latimeria chalumnae and L. menadoensis are the two modern species that have been discovered, and they do not appear in the ancient fossil record. They are considered to be "living fossils" primarily on account of them being the last two living sarcopterygian fish species, a group of fishes that were otherwise known only from fossils that date from the Devonian to the Cretaceous periods.
That scientists believed this entire line to be completely extinct, but were mistaken, is not a challenge to evolution. The theory of evolution never states that a particular line of creatures must go extinct.
Likewise, while the modern species are similar to some of their ancestors evolution also does not require that all lineages must change so radically that they appear to be very different from their ancestors. Creatures that are already well adapted to their ecological niche, for instance, often do not change as radically over time.
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Exclusion (the fact that modern and ancient coelacanths are different is omitted)
Hasty Generalization (if one species is not extinct, that doesn't mean no species is extinct)