The speaker of "The Love Song of J. Alfred Prufrock” by T. S. Eliot tells us more than once that the women "come and go / Talking of Michelangelo" because he wants to convey to the reader that while the speaker/narrator is pondering life in a serious way, these women are, somewhat flippantly at a social gathering, lightheartedly moving from room to room and discussing art and may not be attuned to deeper, more important issues (or don’t care if they are attuned to them).
T. S. Eliot inserts the phrase, “In the room the women come and go / Talking of Michelangelo" at two critical junctures of the poem. The first is after the first English stanza. In the first stanza, the speaker talks of streets “that follow like a tedious argument," and also the evening spread out and likened to “a patient etherized upon a table." Therefore, it is apparent that the speaker is tired with life and even the evening about him makes him think of a person under ether on an operating table, possibly in a life-threatening situation. This sets the somewhat somber mood of this poem as the speaker, a man, thinks about his life—the past and his mistakes, the present and his inertia, and his less-than-enthusiastic view of the future. This is a counterpoint to the pleasant and cheerful evening the women are having.
The second use of the phrase is after the speaker talks about putting on a façade to ready himself to meet people in different situations. This shows the man’s misanthropic and cynical view of life and personal interactions and relationships.
The speaker also talks about there being time for “a hundred indecisions." As such, he is saying that he cannot commit to taking a stand or being resolute. It is as if he’s just rolling through life without enthusiasm and verve or the mindset to be purposeful and clear-sighted enough to make quality decisions. Therefore, he is somewhat like the women who "come and go” and engage in gentle banter as they enjoy a night out with somewhat light conversation. So, in one case the speaker is different than the women. In the other case he is a little like the women.
J. Alfred Prufrock longs to ask, essentially, “What is life all about?” In other words, “What is our purpose in all this theater or drama here on earth?” He looks at life and all its situations and relationships and strivings and wonders if it is all worth it in the end if one doesn’t have a strong purpose and a hope for the future.
The speaker wants to be bolder and more daring. He states that he is really the following type of person: “Deferential, glad to be of use, / Politic, cautious, and meticulous.” Consequently, he longs to ask the above-mentioned questions, as well as, “How can I live a less fearful life?”