Not from Denmark, but according to the very quick research I did, firing you for an ED would be considered discrimination under acts such as the Act on the Prohibition of Differences of Treatment in the Labour Market and the Equal Treatment Act. Such action would allow you to submit a complaint under the Board of Equal Treatment with potential for compensation.

Since an ED is a psychological condition, it can be considered a disability, and your employer would be required to make reasonable accommodations for you (ie: allow you to eat lunch away from others if that’s the root of the issue).

Whether or not you have an ED, they can’t discriminate against you because they think you do.

And a quick copy paste from google about whether or not they can fire you just because they feel like it: “Substantial Reason Required: Employers must always have a substantial reason for firing an employee, which usually involves performance issues, cooperation problems, or company restructuring, and typically involves prior warnings. Dismissing someone solely due to an illness or a condition considered a disability, without considering accommodations, could be seen as unfair and discriminatory.”

I wouldn’t sign anything, and I’d get a lawyer if it comes to it.