@Rin2k and
@PurpleBomber I think it boils down more to manliness. Not in the "toxic masculinity" kind of way but in the "provide and protect" kind of way.
Nania considers Masaru unfit to protect Elizabeth. He is a D rank adventurer and Elizabeth is B rank. He has been hunting rabbits sporadically for a 2 monthss. Meanwhile Elizabeth and Nania have been on the front lines with for 4 years in a party specialized on dragon hunting with 4 vanguards (Orba, Turks, Luven, Nania).
Masaru just confessed his feelings to Elizabeth and agreed to go adventuring with her. This duel serves to prove he can protect her.
Masaru also has the explicit ambition to build a harem and 2 girls have accepted his feelings (3 if you consider Satie but not there yet). He needs to prove the girls and himself he can actually do it, that he can protect and provide for them.
Imagine Masaru loses his duel "shit yo, from now on I will be tagging along with your girlfriend and protect her since you can't. Also I gave up on the love of my life because you suck so thanks for it."
I think it goes beyond "awkward" and gets into "soul draining"