Fats are important molecules and are considered essential to ones survival. Indeed, fats are involved in many of the body's processes which are required for survival. Several key functions of fats in the human body are for energy storage and hormone synthesis. They are the body's preferred source of stored energy and the most efficient molecule for the body to burn. (in terms of energy yield per gram, 9kcals/gram).
The main hormone that fats impact which we are concerned with is testosterone. When calories are restricted, testosterone levels will drop, as the body will suppress its release of anabolic hormones in order to spare nutrients for oxidation (energy production). This makes perfect sense: the body senses it is "starving" and thus it represses it's anabolic hormones to prevent nutrients from being used to increase tissue mass and spares them for energy production.
That's the first hit against testosterone production. Drastically lowering your fat intake is another hit against testosterone production since fatty acids are the substrates for cholesterol synthesis and therefore are also the substrates for testosterone synthesis (cholesterol is converted to testosterone, among other things).
Unfortunately, fats are also easily stored as adipose tissue (body fat) So there must be some type of comprimise between ingesting enough fat for hormone maintenance (and subsequent muscle maintenance) and reducing fat intake enough to decrease body fat.
There has been some research done on the effects of dietary fat on testosterone. The answer to, "how much dietary fat is optimal" is difficult to decipher, as there are major differences in the designs of the performed studies. This makes it difficult to compare them to each other and come up with a "standard" answer.
Several studies concluded that diets low in fat (under 15% of total calories) significantly decreased testosterone levels while diets higher in fat (above 30% of total calories) increased serum testosterone levels.15,16 Rather than continuing with this discussion I will provide a link to an article which covers the subject quite nicely.
To simplify everything that I have said, it seems that one should not lower fat below 15% of daily calories unless they would like to face extreme testosterone deficiencies. Likewise, one should not increase fat to say 40% in order to increase testosterone.
Although fat increases testosterone to a degree, it is important to remember that testosterone is only a small piece of the larger puzzle. There are many other hormones and factors involved in building muscle other than just testosterone. By increasing fat to extremely high levels, there will be less "space" for carbohydrates and protein, both of which are very important for aforementioned reasons.
As with most things in life, moderation is key. In order to keep hormone production regular and fat burning in high gear, while allowing enough "space" to supply adequate carbohydrates and protein for muscle sparing purposes I do not recommend increasing fat above 30% of daily calories.