I think I may know why, make the e noise in feel. Make the same noise with pursed/rounded lips and you'll get what the y sounds like in fyrre.
My recommendation to hear the difference is to use the methods described on fluent forever to learn pronunciation. AKA Anki (the model Anki decks on Fluent Forever are key though)
I bet speakdanish.dk's resource on numbers is probably a better resource for pronunciation than the duolingo TTS
IPA and pronunciation http://ordnet.dk/ddo/ordbog?query=fyrre=S%C3%B8g