Why and how could an organism evolve to make its bones or exoskeleton out of a UTH (Ultra High Temperature) ceramic like TiB2, WC, B4C, or TaHfC?
Is it even possible?
A1: It uses naturally occurring materials.
Your organism does not generate these high temp ceramics within its body. It finds these materials in the environment and assembles them into its exoskeleton. Circumstances in your world lead to geologic production of your ceramics. Your organism finds suitable pieces like a hermit crab finds a suitable mollusk shell. It assembles smaller pieces into a larger one using biological glue. Possibly a good piece might already be in a shape suitable for use - or your creatures have evolved such that the ones that have best fitness are the ones that can use naturally occurring ceramic shapes.
A good exoskeleton will likely far outlast any given individual. The best ones are very old and have been used and improved by successive generations of these creatures.
A2: The ceramic exoskeletons are products of technology.
Your creatures used to be like hermit crabs, finding suitable shells or exoskeletons made by other creatures. Maybe the primitives still do it that way. But your species has tech and makes their own exoskeletons of ceramic. Initially this was simple fired clay but as their tech improved, sophisticated ceramics such as those you propose became possible.
If your creatures do not have the tech to make UTH ceramics, maybe these exoskeletons are made for them by a species that does. Or possibly the artificial UTH ceramic exoskeletons are found in ruins or underground, produced in the remote past for unknown reasons by a species no longer present on the world.
Evolutionary pressure, of course. The same evolutionary pressure that made animals heavier than air learn to fly, trees and plants which find dead with fire having to need the fire to better spread their seeds, and so forth and so on.
One of the possible path is that one organism starts to embody some of those chemicals, like Ta, B, Ti, W, as nodules to get rid of them and have them away from their metabolic paths.
Those nodule, accumulating in bones or shell or exoskeleton, make that organism harder to kill, thus giving it a competitive advantage.
Repeat over many generations.