One of the issues. There are number of others. For example, VAT is a value-based tax. A VAT cut gives the biggest savings to people who spend the most. Since wealthier people typically spend more, they would save more money in absolute terms. For example, a family with a food budget of 3,000 kr. would save 300 kr., while a family with a food budget of 8,000 kr. would save 800 kr. Politically, some parties might prefer tax breaks that focused on lower-income groups.
Another issue, will the cost savings actually be passed on to the consumer?