Everywhere I look online says the brain is about 60% fat. But when it comes to water, I see numbers like 70-75%. One webpage even makes both those claims back to back! That doesn't make any sense. So what is it, really?
Whenever you see a percentage, you should think "Percentage of what?". Not doing this is usually at the root of the trouble people get into with percentages.
The water and fat percentages mentioned in the question are certainly not percentages of the same thing. The sources of the figures should make clear what the percentage is of, but non-scientific writing quite often fails to do this.
In the paper "Lipid composition of the normal human brain", there is a table giving percentages of water and lipids (fats), and at the bottom of the table it says:
All values, except water, are expressed as a percentage of dry weight.
This is a common approach, as, for example in this table from a textbook the lipid percentages are also given as percent of dry weight. This is convenient because water is such a large part of most organisms, and also dry weight is what is usually measured in the laboratory.
Thus the water percentages you are seeing are presumably percentages of total weight, and the fat percentages are percentage of dry weight. You can convert the latter to percent of total weight by multiplying by the dry percentage of the brain, which is what is left when you subtract the water percentage from 100%.
Thus, assuming say 73% of total brain weight is water, the 60% fat figure would translate to about 16% of total brain weight is fat.