is not about a romance at all, but about two beggars, one blind and one lame, who have been travelling together for forty years, depending on each others' skills and abilities. They arrive at the well of Saint Colman who offers them the choice: "Will you be cured or will you be blessed?" The blind man chooses the cure and the lame man the blessing. The blind man leaves on his own at the end of the play but the Saint accompanies the lame man, who even blesses the road by dancing despite not having been "cured." Interpreting the poem as about Yeat's romance with Maud Gonne does seem to take it out of context, although readers unfamiliar with the play frequently do so.

The key oppositions in the poem are between the celestial and the terrestrial worlds, with the cat being a link between the two. The black cat is the color of the new moon. The moon itself does not radiate light, but only reflects the sun's light, changing brightness as it changes phases. The cat too is only seen when illuminated by the external light sources such as the sun. Not only are the cat and the moon similar in that they are only visible to humans in so far as they are illuminated by external sources, but also, the cat's pupils change phases from round to crescent like the moon. 

Yeats' poem reflects his own complex synthesis of mysticism, philosophy, astrology and occultism. Within this system (which is not entirely coherent), the black cat would have a unique and intimate connection with the moon. Rather than think of the cat as Yeats and the moon as Gonne, the key opposition is the light of Yeats' poetry and language and reason themselves which are a masculine principles revealing and illuminating the cat and moon, who are celestial and terrestrial aspects of a type of spiritual principle or wisdom. 

Another key area you might want to explore is the relationship between inner and outer sight. While the blind man can see the sky and grass and color of the sheepskin jacket the lame man stole, he cannot see the Saint, who can only be seen by the lame man who chose to be blessed. 

The cat Minnaloushe can see the true nature of the sacred moon with his ever changing eyes, and he is also described as "wise". This notion of an inner or sacred vision that sees the true nature also appears in several of Yeats' explicit love poems such as "When You Are Old" which discusses how while others only saw external beauty, the narrator saw into the beloved's true inner beauty. Here both cat and moon serve as emblems of that hidden inner beauty only revealed by the illumination of true love or spiritual wisdom.

The theme of “The Cat and the Moon” might be opposites. In the poem, W. B. Yeats depicts the two figures as not having much in common. Besides their fundamental differences (a moon is a satellite object; a cat is a mammal), there’s an array of divergent characteristics. It’s as if the moon and the cat are people with clashing personalities. The cat is lively and nimble; it wanders and wails throughout the land. The moon appears dispassionate and covert; its light is “cold,” and its phases aren’t as explicit as the movements of the cat.

In addition to the theme of opposites, it’s possible to claim that the theme of attraction is important to the poem. As incompatible as they seem, something attracts them to one another. The moon’s light stimulates the cat. Meanwhile, the cat’s dances inspire the moon to try out something other than its “courtly fashion.” The ending of the poem provides further evidence of the attraction between the cat and the moon. The cat and the moon make eye contact as if they’re inevitably drawn to one another.

Another way to analyze this poem is through an autobiographical lens. The theme of opposites and attraction might relate to Yeats and his love for Maud Gonne. Minnaloushe was the name of a cat in Gonne’s family. Like the cat and the moon, Yeats and Gonne were enticed by one another even though they were somewhat mismatched. Similar to the cat and the moon, Yeats and Gonne’s romance remained elusive. They each married someone else.