Not much detail behind the politics and interests behind the decision. It looks like short-term economic concerns (increased food prices, impact on Danish agriculture industry) were the main causes. The measures were not in place long enough to have any discernible health impact, and no information whether consumption of high-fat foods decreased or not.
Some of the medical experts cited noted that sugar taxes were more ‘plausible and defensible’ than fat taxes.
An additional article, outlining some of the economic and other interests behind the change in policy: