Beowulf's warm welcome from Hrothgar is not echoed by Hrothgar's "thyle," Unferth. Now a thyle has no real equivalent these days, but Wikipedia has a short, helpful article on them.
I picture a thyle as a kind of prosecuting attorney in the King's court. If someone makes a statement of fact, the thyle will try (test) it. If someone makes a statement of purpose, the thyle will make sure it is wise or achievable. Looked at this way, Unferth is doing no more than his duty when he casts doubt on Beowulf's ability to survive even "the length of a night" against Grendel.
On the other hand, the poem says directly that Unferth's motivation was jealousy: "he could never say that another man/could accomplish more on Middle Earth/or gain under heaven higher acclaim."
Another insight into Unferth is this description of his challenge to Beowulf, "He unbound runes of battle." This seems to mean that he is showing a dislike or anger that had been secret until then (like revealing rune letters so that their secret meanings could be read).
Unferth chose to illustrate Beowulf's limitations by telling about a swimming (or rowing) contest that Beowulf had had with his friend Breca. Since Beowulf could not even beat Breca, he says, he cannot be expected to beat Grendel.
Now, as to the choice between Beowulf swimming and Beowulf rowing, I'm depending on remarks made by Ben Slade on his website as a footnote for lines 506-81. First, he says, most of the words that support the "swimming" idea have more general meanings: on sund is translated swimming, but generally means in the (ocean) sound; and reon is translated as swimming, though it means generally to travel across water; and line 581 has wudu (wood, a word used to describe ships), but this is amended to wadu (water) to make the swimming interpretation work. I've accepted the "rowing" version because the last point follows the plain meaning of the text and the other words and phrases are ambiguous.
Finally, we see how Beowulf, the big guy himself, responds to being challenged. Pretty well, I'd say. He begins with a formal Hwaet!, just like the Beowulf poem itself, meaning that he is going to answer formally and (most likely) at length. He then begins to retell the rowing contest story in more detail. His story gives us the first clear view of Beowulf's superhuman strength (although, to be fair, Breca emerges creditably from the water, too). It turns out that Beowulf was slowed down by an attack by a sea creature that dragged him underwater.
Beowulf has more to say on this in the next Fitt, and I will make a few notes about the custom of "flyting" then. In the meantime, here is Unferth's challenge and the beginning of Beowulf's response.
IX. UNFERTH CHALLENGES BEOWULF. HE REPLIES.
Then Unferth spoke. The son of Ecglaf
who sat at the feet of the friend of Scyldings 500
unbound runes of battle. Beowulf’s quest,
the brave seafarer’s, upset him greatly
for he never could say that another man
could accomplish more on Middle Earth
or gain under heaven higher acclaim.
“Are you the Beowulf, Breca’s rival
“who tried to best him on the broad ocean
“for no reason but pride? You risked the waters
“for a silly dare. In the deep sea
“your lives could be lost. No living man— 510
“not foe nor friend—could force a retreat
“from that crazy stunt of crossing the sound.
“There your arms stretched over the streams,
“measured sea-lanes, mixed the waters,
“gliding over the sea. There were surging waves,
“winter whitecaps. In the water’s hold
“you strained seven nights. He stroked better,
“with greater might. As morning broke
“combers beached him on the Battle-Reams’ coast,
“which he left to find the land of his birth, 520
“loved by his people, the land of the Brondings,
“the fair fortress of his folk and kin,
“his towns and treasures. Truly it seems,
“Beanstan’s son’s boast had come true.
“So I sense the result will be somewhat worse—
“though you won the fights you waged before
“in grim struggles—if you stand up to Grendel
“and lie in wait the length of a night.”
Beowulf spoke, the son of Ecgtheow.
“NOW. Far too much, my friend Unferth, 530
“and with too much beer you told of Breca,
“tales of his trip. The truth is this:
“my might at sea was more than his;
“my peril on the waves surpassed all others’.
“While just half-grown we had agreed
“and exchanged boasts, both of us still
“in our youthful years, that beyond the shore
“we would risk our lives, as we rightly did.
“As we rowed the sound, our swords were bared
“and held in our hands to have a defence 540
“from whales, as we thought. In no way could he
“float far from me over flood-waves
“as the faster on water, nor would I leave him.
“We stayed together, going over the strait
“through five full nights, till forced apart by waves.
“The angry water, the iciest weather,
“the darkening night and the north wind
“war-grim rushed us. The waves were rough.
“Then the sea fishes’ fury was stirred.
“An aid against foes, my armoured shirt, 550
“strong and hand-linked, helped me withstand them,
“safeguarding my breast, my braided sark,
“adorned with gold. I was dragged to the sea-floor
“by a hated foe holding me fast,
“grim in his grip, but it was granted to me
“that I could mark this monstrous creature
“with my keen blade. My blows curtailed
“the monster’s life through my might of hand.”