Several explanations have been offered. The simplest explanation is that
the leitmotiven are not as closely tied to non-musical ideas as many
people have thought; in other words the reason for Wagner using this
melody at this point could be purely musical. Other explanations try to
find a link between Alberich's renunciation of love, and later appearances
of this motif: Fricka's condemnation of Wotan's treatment of Freia,
Siegmund's drawing of the sword, Wotan's farewell to Brünnhilde and her
refusal to yield the ring. 

The occurrence in 'Die Walküre' act one has been regarded as problematic,
for example by Cooke in his book 'I Saw the World End'. It was suggested
that this is an example of dramatic irony: the sword-redemption is an
ironic moment, not only because of events in the immediate future, but
because for the first time, on a human level, Wagner reveals and
celebrates the protagonistic force (love) that will overcome worldly and
godly power. 

Discussion of what this motif might signify usually results in alternative
names being suggested for a motif that von Wolzogen called,
'Renunciation'. The names suggested by participants in hmcw have included
'Acceptance of Destiny', and 'Power of Love'. Another suggestion was that
since Siegmund's words are "Holiest Love's Deepest Distress", Wagner is
attempting to draw our attention not to Siegmund's distress, but rather to
the more far reaching distress of love itself, as it is threatened by the
loveless machinations of Alberich. 

Monte Stone, an occasional participant in hmcw, has included commentary on
this motif on his 'Ring-disc' (see B above). Stone notes that in one of
Wagner's drafts for 'Das Rheingold', he appears to refer to this motif as
'Love-Curse' (Liebesfluch), which is the name used by Darcy in his book
about this drama. Stone observes that Alberich goes beyond the
renunciation of love -- Alberich curses love itself. Later, "during
Siegmund's passionate affirmation of love, we are reminded of the curse
under which love labors, and we are given a brief but grim foreshadowing
of the fate in store for these lovers".