Can the human body create glucose out of fat?
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).