I read conflicting views about whether or not the human body can create glucose out of fat. Can it?
Only about 5–6% of triglyceride (fat) can be converted to glucose in humans.
This is because triglyceride is made up of one 3-carbon glycerol molecule and three 16- or 18-carbon fatty acids. The glycerol (3/51-to-57 = 5.2–5.9%) can be converted to glucose in the liver by gluconeogenesis (after conversion to dihydroxyacetone phosphate).
The fatty acid chains, however, are oxidized to acetyl-CoA, which cannot be converted to glucose in humans. Acetyl-CoA is a source of ATP when oxidized in the tricarboxylic acid cycle, but the carbon goes to carbon dioxide. (The molecule of oxaloacetate produced in the cycle only balances the one acetyl-CoA condenses with to enter the cycle, and so cannot be tapped off to gluconeogenesis.)
So triglyceride is a poor source of glucose in starvation, and that is not its primary function. Some Acetyl-CoA is converted to ketone bodies (acetoacetate and β-hydroxybutyrate) in starvation, which can replace part — but not all — of the brain’s requirement for glucose.
Plants and some bacteria can convert fatty acids to glucose because they possess the glyoxylate shunt enzymes that allow two molecules of Acetyl-CoA to be converted into malate and then oxaloacetate. This is generally lacking in mammals, although it has been reported in hibernating animals (thanks to @Roland for the last piece of info).
To be more detailed it is the irreversibly of the reaction carried by Pyruvate dehydrogenase that makes the conversion of the fatty acid chains to glucose impossible. The fatty acids chains are converted to acetyl-CoA.
Acetyl-CoA to be converted into pyruvate need an enzyme that can do the Pyruvate Dehydrogenase's inverse reaction (in humans there is no such enzyme). Than the pyruvete inside the mitochondria is converted into glucose(gluconeogenesis).