Why did Eliot title his poem a "Love Song"?

The fact that T.S. Eliot titled his dreary poem a love song is an example of irony. For anything to be considered a love story/song, it must follow a certain layout. In T.S. Eliot's poem, there is only one main character who argues with himself throughout the entire poem, and for something to be considered a love song, it must involve both a man and a woman directly. This poem is the exact opposite, only showing Prufrock to be arguing with himself. This struggle is, in fact, an aspect of a love story, but because in his case it is a struggle within himself, it doesn't count. Another important aspect of a love story is the ending. For something to be officially considered a love story or a love song, it must leave the audience feeling somewhat emotionally satisfied. T.S Eliot's "love song" does the exact opposite. His use of personification and imagery to paint a dark scene in the readers mind never takes a significant turn to the cheer the reader up towards the end. The dreary tone remains throughout the entire poem. If he had changed it to represent that Prufrock turned out happy in the end, and the readers felt satisfied, this poem would at least fulfill one aspect to bring it closer to being an actual "love song". It is ironic that this poem is titled a love song because Eliot goes against all actual aspects of a love song, which succeeds in throwing the readers off and leaving them wondering his motives in titling it a love song.