Egen is not pronounced correctly. Google Translate does it as it should. https://translate.google.dk/?hl=datab=wT#da/en/egen
Some people would consider "their" to be grammatically wrong because it is technically a plural pronoun, but many people (especially younger people) would not have a problem with "their" and would likely even prefer it to "one's". Personally, as a native English speaker, I would never use this sentence the way it is phrased and I would use "their" instead.
I am not a language person by trade, but I am a dane. I would say that it definitely is not an idiom, but rather inappropriate sentence for learning a language I think. That sentence is quite quirky, even in both languages in question, and might only lead to unnecessary confusion.
I guess the author thinks that a sentence with the danish word "ens" should be used in a context where it does not mean equal.