They're certainly inferior to Lorelai Gilmore, the bright, witty firebrand who single-handedly raised the cleverest girl in Stars Hollow while working her way from chambermaid to manager of a local inn, gaining a business degree in the process. Sure, at times she's a little over-invested in her daughter Rory's life (like when she sleeps over during Rory's first night at college), and she can be rude and selfish, especially when it comes to her own parents (although not entirely without reason). But she's also the fun mom who'll take you to concerts and and sneak you into her bachelorette party by pretending you're an international supermodel.
No wonder, then, that her parenting prowess doesn't only extend to her own child, but to those of the men she knows and dates, as well. Her friend Luke is (naturally) transformed by single fatherhood, first when he becomes a surrogate dad to his 17-year old nephew Jess, and later when he finds out he has a 12-year-old child from a past relationship. But unlike Lorelai, he doesn't learn to be an effective parent on his own: he needs her help. When Lorelai warns Luke that Jess is a bad seed, he's incensed, but she's proven right when Jess accidentally crashes Rory's car, breaking her arm in the process, and later when he drops out of high school and runs away.
When Luke's daughter April tracks him down, his first reaction is to keep her from Lorelai, to whom he's now engaged, while they bond. Only when Luke struggles to entertain April and her friends at her birthday party and Lorelai saves the day does he realize he should have involved her earlier. Later, when he and Lorelai are estranged, she's the person he turns to for help in his custody battle, and his admission that he was wrong in not letting her see April is an essential element of their rapprochement. In her next serious relationship with (ugh) Christopher, Rory's dad, Lorelai again sticks her nose into her partner's parenting, telling Chris first that he's spoiling his young daughter Gigi, and later that his plan to send Gigi to visit her mom alone is untenable. After some initial resistance, Chris bows to her superior knowledge and they're able to get married; his acknowledgement of her supermom status cementing their relationship.
Neither Lorelai nor Rory appear to harbor any bitterness toward Chris, despite the fact that he spent the majority of Rory's childhood riding his motorbike from one town/woman/failed business venture to another, rarely remembering to call. There's the sense that his actions don't really matter: as long as Rory has Lorelai, her dad is just an optional extra. Lorelai's first fiancé, Max, is clued into this when he wonders what role he'll take on when he becomes Rory's stepfather, and Lorelai tells him he won't have one.
She's not the only strong solo mom on the show. Although she's been married since her early twenties, Emily Gilmore was at times a single parent due to her husband Richard's work abroad. She was an upper class stay-at-home mom, in control of hiring staff, arranging meals and parties and keeping the couple's social diary. Although she has very different values to Lorelai, she commands respect. (Richard is never so abhorrent as when he belittles her lifestyle and the sacrifices she's made to support his career.)
Mrs Kim allegedly has a husband, but functions as a single parent, taking sole responsibility for Lane's upbringing. And of course there's Anna, April's overprotective mom, another striking, young-seeming small business owner with a self-confident manner who eventually relieves Luke of all but occasional parenting duties when she moves with their daughter to New Mexico. Probably because her first husband (and Jess's dad) Jimmy turned out to be such a feckless loser, Liz's first reaction on discovering she's pregnant is is to kick out her husband T.J. and go it alone.
The women in the show who aren't moms are tough cookies, too: Paris Geller, Babette, Miss Patty, and the Independence Inn's owner Mia are all strong women whose male partners fade into the background beside them. And she's not a single mother like Lorelai, but Rory still follows in her mom's footsteps when it comes to telling other people's parents what to do: after her boyfriend's dad refuses to visit him in the hospital following a serious accident, she gives him an ear-bashing Lorelai would be proud of, and he relents.
Although it's great to see a show where single moms are far from victims and although Gilmore Girls is progressive in several ways (from not making Melissa McCarthy a walking fat joke to having a female town mechanic and more people of color than most CW shows of the time), when it comes to parenting it's a shame there's such an imbalance. A matriarchy is sometimes espoused as a feminist ideal, but the fact that none of the single dads in Stars Hollow can cope without a woman's help encourages the idea that women are inherently better equipped to be primary caregivers, further perpetuating society's limited and heteronormative ideas about gender roles.