Hrothgar's ancestor Shield is essentially an orphan, or at the very least, disowned by his people. This is the Founder made strong by scarcity. Note that Hrothgar is the fourth generation after Shield¹.

As a young prince, Shield's heir is known for giving. While his father lives, his position is protected by his father. When his father dies, it is implied that the heir's position will be protected by the implication of his might. Someone with power must give freely, so that his succession is secured². To get power, let your actions be aspirational.

Grendel, from a group living in scarcity due to exclusion³, starts preying on Hrothgar's decadent (Hrothgar's aim was to build a great mead-hall, a center of entertainment- he is known as 'giver of rings', a bestower of material wealth) territory. His first attack occurs when Hrothgar's people (ostensibly warriors) are caught drunk and sleeping with no one on watch.

Grendel's aim is punishment, and he will not negotiate with the Danes. Hrothgar's (relatively) soft life has not prepared him to face the likes of Grendel.

The coalition of elders of the Geats do not try to stop Beowulf from helping⁴ Hrothgar. In fact, they encourage him to leave. It may be that they're trying to get rid of someone as dominant as Beowulf. Beowulf's men, as hardened as they are, show up in full battle-rattle without asking Hrothgar permission. This is a breach of manners, like the United States sending a Quick Reaction Force to the UK without letting them know in advance.

Beowulf takes advantage of Hrothgar's distress here, and offers to solve his problem for him. Beowulf has a pre-existing relationship with Hrothgar- Hrothgar knew his father. In fact, Beowulf's father owes something to Hrothgar. Hrothgar paid down some of Beowulf's father's debt.

Despite the underlying mismatch of martial power (I get the impression that Beowulf could take Hrothgar), he asks Hrothgar for permission and observes all the other courtesies (besides breaking the initial one by landing without announcement). Basically, Beowulf gives Hrothgar the recognition and credit for his own might.

Grendel has been fighting without weapons, and in order to further improve his reputation, Beowulf claims he'll fight Grendel without weapons. Winning the battle is not the most important thing here- the how of how he'll win the battle is more important for the strategy of his life. A decisive victory impacts how the population sees you, and the source of power is ultimately the population itself. If his reputation grows, he effectively gains more power. Beowulf reminds everyone of the stakes: if he loses, it'll be shitty for everyone. This gets the emotional energy of the crowd behind him.

We find that past warriors who vowed to defeat Grendel often partied in Hrothgar's luxurious meadhall, and this is when Grendel would catch them with their guard down. Loss begets loss, and Hrothgar is losing the support of his people.

Unferth, who might be one of the biggest fish in Hrothgar's pond, feels threatened by Beowulf's presence. To protect his position, he attempts to downplay Beowulf's achievements- including a swimrace with Breca. Since Unferth isn't strong enough to take on Grendel, no one can be.

Beowulf suggests that Unferth is too drunk, and clarifies that he and Breca are longtime friends who consistently challenge each other to do better. Beowulf clarifies that he killed creatures of the sea in order to win that race, and in the end Breca and Unferth are both sore losers. Beowulf points out that Unferth's wins are against his own people. If Unferth was strong enough, Grendel wouldn't be doing as much damage as he's doing.

"a daunting man, dangerous in action and eager for it always"

Beowulf takes responsibility for Grendel when he speaks to Wealhtheow (Hrothgar's wife, the Queen). He tells her he will either get the job done or die trying.

Hrothgar cedes responsibility to Beowulf, and promises Everything.

Beowulf knows he's on reality's side.

Grendel is from the wild⁵ and does not fight with modern tools of war. Beowulf decides to fight Grendel on his own terms, so that the victory is decisive. If Beowulf wins through superior equipment, his victory will be worth less. If Beowulf in circumstances that are different from the ones past warriors lost in, his victory will be worth less. This is why he sleeps in the meadhall, instead of setting up an ambush for Grendel.

Civilization, for all its softness, is superior- this is the message that Beowulf intends to send.