My brain and focus is just way better running on fat than on glucose.
Your body runs on sugar not fat. Fat will be transformed into sugar to be used as energy in your body. With that said, it won't create a huge spike in your blood sugar like drinking a soda, and won't cause a giant release of insulin.
Essentially:
Glucose ->[0] pyruvate ->[1] acetyl-coa -> TCA cycle
Fatty acids ->[2] acetyl-coa -> TCA cycle
Other times fat absolutely is converted to sugar. It all depends on the metabolic needs of the body and one building blocks are available, and what protein "workers" are able to use the ones that are available.
For example, fatty acid synthase converts acetyl coa back to a fatty acid [3].
[0] Glycolysis: http://en.wikipedia.org/wiki/Glycolysis
[1] pyruvate dehydrogenase: http://en.wikipedia.org/wiki/Pyruvate_dehydrogenase
[2] beta oxidation: http://en.wikipedia.org/wiki/Beta_oxidation
If you are referring to gluconeogenesis, yes, fat and protein can be converted to glucose but the amounts are fairly negligible. If you eat fat or have fat the body will convert the fat to ketones and use that in the absence of glucose. It's a much more efficient metabolic pathway than going through gluconeogenesis. The vast majority of the body functions quite well on ketones for energy. Most people are not able to metabolize fat at the rates required to avoid fatigue without undergoing ketoadaptation though. It takes anywhere from 3 days to 3 weeks depending on the individual and seems to be correlated with insulin resistance.