You don't have to, but I wouldn't recommend for a variety of reasons.
1. The battle system is rougher in Eternal Wings, so playing Origins after it would give you more appreciation for it.
2. Some of the characters in Eternal Wings get some extra screen time in Origins, which means you'll get to see more about their past.
3. There's a reveal in Origins about the final boss in Eternal Wings. Not having the knowledge from Eternal Wings gives it far more weight.
4. Similar to the battle system, little things like voice acting, navigation and the like are much more polished in Origins.
Both are great games. If there's absolutely no way that you can play Eternal Wings, it's fine to play Origins. It just wouldn't be as impactful.