You're right that Arawn didn't explain his actions, but if he did you should consider it a red herring. The most important part of this story is that the hero and the "otherworld" character swap places. From the footnotes of your online translation:
As this point the plot begins to take the form of another stereotyped
narrative mytheme, equally familiar throughout the Celtic world. The
Otherworld Sojourn, as we might call this scenario, could take a
number of forms: but always followed the same basic gist: the mortal
protagonist is lured to an Otherworldly domain, where they
subsequently abide for a period of time. This occurs at the
instigation of one or more of the Otherworld beings, and often follows
a Chase of the White Stag introduction, or some variant thereof.
The purpose of Pwyll's sorjourn in the Indigenous Underworld is to rid
Arawn of his 'oppression': the rival king Hafgan ('Summer-Bright')
with whom he is locked in a ongoing and irreconcilable conflict. A
further example of mortal interventions in Otherworldly conflicts of
this kind in the Celtic world include Arthur's adjudication of the
seasonal dual between Gwynn ap Nudd and Gwerthyfyr ap Greidawl for the
hand of Creiyldyd, on the Calends of May. In this and other respects,
the plot of The Sickness of CuChulain and The Only Jealosy of Emer
follows this First Branch episode even closer: complete with the
'Chase of the White Stag' entrée. This narrative can be summarised
thus:
[it compares the story with another story]
Like Pwyll, CúChulainn finds himself indebted to Otherworld powers as
a result of abusing magical animals on a hunting expedition. Like
Pwyll also, this encounter carries the appearance of having been
contrived and instigated by the Otherworld agency. The measured
responses of Arawn ('I know who you are...'), the location and timing
of their encounter, and its favourable outcome for the Annuvian king
suggest that the event was no coincidence. Like Cú Chulainn, Pwyll was
in effect drawn and entrapped by the otherworld powers involved. And
both were required to visit Underworld regions where they were obliged
to lend their assistance as mortal warriors in the magical
protagonists' struggles for power. Interestingly as well, the Irish
Manawydan - Manannan mac Lír - features in this same story as the one
time spouse of the heroine involved. (As we shall see in subsequent
chapters, Pwyll and Manawydan become linked in a similar way).
This is the most relevant section:
That the denizens of the Indigenous Underworld should be so in need of
the military prowess of mortal warriors is another motif not
unfamiliar within the Celtic world and beyond. The well known myth of
the aversion of faery-folk to iron is an example of the ambiguous
power-relationship between themselves and the mortal world. The
Indigenous Underworld, however, while being mysteriously vulnerable in
certain respects, was clearly a source of danger when it came to
magical initiatives. The trade-off of these respective strengths and
weaknesses is a frequent theme in fairy tales and popular magical
tales from around the world. It was within this tradition that the
narrative of much of the Mabinogi would have been understood.
The narratives produced by animistic belief systems often focus on the
acquisition of power, in its elemental-magical form. The struggle for
possession of this substance of power is typically waged by any
variety of means: trickery and cunning prevailing as frequently as any
other stratagem. In this episode Pwyll is consummately manipulated by
the Underworld agent who thereby obtains his power, which becomes
harnessed to the latter's own agenda in the arena of Annuvian
politics. Through an act of impulsive foolishness (significantly, as
we shall see, involving the dog and the stag), the ironically-named
Pwyll (see p ##-##) had inadvertedly placed himself in a chain of
events, which would ultimately result in a mysterious fusion between
Dyfed and Annwn.
This story is about the somewhat coercive relationship between the "otherworld" and the real world. I think it's just as important to the story that Arawn (the otherworlder) takes Pwyll's (the human's) place in the real world: both the otherworld and the real world have their strengths and weaknesses, and this story is about travelling between the two, and about man's relationship with spirits.
The purpose of god's and spirits isn't to do everything themselves, but (in this story) to coerce and trick mortals into doing things for them. A specific logical reason why Arawn needs Pwyll doesn't exist, because the point of this story is that it's an example of the interactions between the spirit and real world, and not that "Arawn needed Pwyll because Pwyll is really stealthy."
