"— Don't mope over it all day, he said. I'm inconsequent. Give up the moody brooding." Mulligan seems graciously self-deprecating here, but he is, in effect, saying that Stephen should grieve more moderately and less irrationally, and the novel manages to insinuate, by multiple allusions, that his motives are quite selfish. Although the word "brood" prompts him to quote immediately afterward from a gentle and goodnatured poem by Yeats, the chapter's ongoing allusions to Homer's Odyssey and Shakespeare's Hamlet link him to less savory advice-givers.
As Thornton notes, Stuart Gilbert observed in James Joyce's Ulysses that the brooding likens Stephen to Telemachus. Gifford adds that it likens him to Hamlet, whose mother urges him to get over his grief and get out of his mourning attire. If so, then Mulligan plays the roles of Antinous, Claudius, and Gertrude, urging the young prince to get over his grief and resentment because it suits their selfish purposes. These three urge good cheer because good cheer affirms their dominant social position and does not irritate their bad conscience. Mulligan occupies exactly the same position.