Does eating high fat foods cause gout or just make it worse?

Neither: Gout is caused by too much uric acid in the blood. Eating foods high in fat will not affect gout. Food high in uric acid, like steak, will cause gout to flare up. So the problem with steak is not the fat but the uric acid in the meat. The cause of gout is mostly genetic predisposition coupled with the high uric acid diet. Also some medications, diuretics for example, can cause gout to flare up.

Worsens it: Gout is a metabolic disease of purine metabolism. It is worsened by high fat and protein load as well as alcohol. A primary dr should be able to give recommendations on dietary restriction, hydration and possibly medication to help limit the acute flares of gout.