The reason might be as trivial as "we don't want to spend extra money on the necessary equipment and training". Not something fundamental.

After all the other airline has a good safety record, which indicates that raw risk isn't the reason.

I'd really love to hear what you think it is.

I don’t know if you didn’t read or didn’t believe what the other poster said about Atlantic Airways, that they have the equipment to manage the fog and the ability to refuel in Iceland and therefore can try again the same day if necessary. The implication being that SAS have neither - that’s presumably the ”reason they choose to do what they do”.

It’s not unreasonable to think that Atlantic Airways, being a Faroese airline, are better equipped than others to get people to the Faroe Islands.