Despite being more youthful in appearance than her cousin, Superman, Supergirl is actually older than him. Though it hasn't always been the case, most versions of the two have interpreted Kara as being chronologically older than Clark, while being biologically younger. The unique ties they share shines a light on how such a shift has affected the two's family dynamic.
Supergirl has been a part of Superman's cast since she first appeared in Action Comics #252 in a story by Otto Binder and Al Plastino. Emerging from a capsule, Supergirl told the harrowing story of her escape from Argo City, one of Krypton's last remaining civilizations. After witnessing a recording of Superman and discovering he was from Krypton, Kara's parents sent her to Earth to learn from the Man of Steel, unaware the hero is actually Kara's cousin.
While the Silver Age story established Supergirl as being born after Krypton's destruction, more modern takes on Kara have presented her as a teenager at the planet's pivotal moment. In Superman/Batman #9 by Jeph Loeb and Michael Turner, Kara discusses her father's attempt to save her with a ship similar to her cousin's. However, Kara's ship was caught in a meteor made of Kryptonite, which she believes kept her in a state of suspended animation for decades. By the time the ship was freed and could relocate to Earth, Kara was virtually the same age, while her baby cousin had become a fully grown adult. A similar, but altered, origin was shown in the New 52, where Kara was intentionally placed in a stasis pod by her father, which orbited the solar system before sending her to Earth.
So despite the Silver Age outlier, it's accepted that Supergirl is indeed older than her cousin, at least in terms of who was physically born first. However, no matter how many years Kara can claim, the end result is her being younger than Superman. This is not the most fair of circumstances, considering Kara has often been portrayed as the more inexperienced of the two while on Earth.
Age generally plays a large factor in families, with older members encouraged to provide guidance to younger generations. But that doesn't exactly apply to Supergirl when her cousin has experienced far more in life thanks to her years in stasis. In fact, her origin stories are often accompanied with Clark teaching her to acclimate to Earth. So while it may be fact that Kara was born first, the reality is that their relationship is reversed thanks to an unfortunate set of circumstances.
All of this isn't to say that Supergirl is unassured or has no idea what she's doing as Kara has shown growth into quite the confident hero every time she's emerged from suspended animation. But Superman has been around the block a bit longer than Supergirl, giving him a perspective she hasn't had the chance to live through yet.