Spoiler: he didn’t.
Summary:
- Denken implied that he could take on Frieren during the Mage Exam arc, which obviously isn’t true.
- It was just a bluff to protect innocents.
- Denken might have wanted to see how strong Frieren actually was.
During the First-Class Mage Exam arc in Frieren: Beyond Journey’s End, Denken decides to go against Frieren’s team in the first test. The task is to capture a bird, and he wants to get a bird from them instead of searching for his own.
It seems that he was confident that he could fight Frieren on at least equal terms — but why did he think that? It’s not like him to misjudge his opponents so badly.
Frieren is obviously much stronger
Frieren herself is a legendary mage who was a member of the party that defeated the Demon King. She lived for hundreds of years and is extremely experienced — the only reason she’s not a first-class mage already is that she never bothered to actually receive official qualifications.
We haven’t even seen Frieren’s full power in the anime yet. She simply doesn’t need to go all-out, as she never faces enemies that actually threaten her.
In the latest episode, we’ve seen some of her more powerful spells when she was fighting her double, and even then, she probably could’ve used more destructive magic — she just couldn’t because Fern would be in danger.
It was actually just a bluff to protect others
Yes, Denken is also extremely powerful. At the start of the exam, he’s a second-class imperial mage. He’s cunning and experienced, and is definitely one of the strongest participants of the exam — yet for him to consider Frieren an opponent he could realistically defeat was… somewhat foolish.
However, fans point out that he actually wasn’t planning to defeat Frieren: he was simply bluffing. By doing that, he would protect Kanne and Lawine from his own teammate, Richter.
Denken thought that becoming a first-class mage wasn’t worth it if you had to kill others — and that’s completely understandable, seeing as he already knows the value of human life. He lost his wife in the past, and is actually very considerate of others.
He wanted to see how much stronger Frieren was
Some fans also speculate that Denken somewhat wanted to see Frieren in action to fully gauge her strength. He fully understood she was stronger than him: he just didn’t know how much stronger she was.
That said, the second time they could have confronted each other, Denken simply refused. He already knew he stood no chance, and he doesn’t fight for the sake of fighting. Sometimes, the way to win is just not fighting at all