Nature produces cis fats exclusively (someone may prove me wrong with some weird example.) This is why unsaturated fats such as vegetable oil have lower melting point than saturated fats of the same MW (the cis double bonds lead to a more compact molecule which gets less tangled with its neighbours.)
The reason nature produces cis bonds is due to the enzymatic mechanism in which these bonds are produced. Therefore this is down to reaction kinetics, and as often happens the product which is not the most thermodynamically stable of all possible products is produced. It just has to be more stable than the reactants.
When fat is artificially hydrogenated with a metal catalyst (for example nickel) to increase its viscosity/raise its melting point (to turn vegetable oil into margarine) some of the cis double bonds that escape being hydrogenated are able to change from cis to the more thermodynamically stable trans. These trans fats are unnatural and are therefore widely claimed to be unhealthy.