Why do we have to get them from our diet, and if they aren't taken in our diet we will face disease? Then why we don't have the enzymes which are require for EFA synthesis?
Well, the essential fatty acids that humans fail to produce are not the same ones that other species fail to produce. For example, while cats produce their own Vitamin C and will therefore never develop scurvy, they can't produce their own taurine and will become sick if they don't consume enough of it.
To answer why a species might lose the ability to produce an essential amino acid, you have to consider what that species is eating most of the time. If its diet is rich in the amino acid anyway, individuals who lose the ability to synthesize it either feel no cost or--possibly more likely--even benefit by not wasting resources synthesizing compounds that may be abundant already in the diet and must be excreted if unused.
Turns out that this loss of ability to synthesize your own fatty acids is a particularly common consequence of evolving parasitic lifestyles, which makes sense: if you're just stealing someone else's acids, why bother to produce your own? Even outside of parasites, there's some interesting discussion on why the nine amino acids essential to all animals might have evolved from a genomics paper here, discussing which amino acids you really do have to make on your own and which you can get away with consuming depending on your species' lifestyle and dietary habits.