"Love is A Distraction" - They have a job to do and can't risk being distracted by something as petty as a love life.
"True Love Doesn't Exist Anymore" - They are absolutely sickened by the sexual and/or romantic values of most if not all of the other characters, and find it sickening that anyone would even think that they would stoop to the same level. May come off to passers-by as merely haughtiness (and it certainly can be), but if the character in question remembers a world or a time in which their values still existed, were far more common, or were maybe even the standard, then it would be more accurate to say that the character looks at the current world as a Wretched Hive and/or Vice City and its inhabitants as immoral, awful people. Can often overlap with Rebellious Rebel and Black Sheep. Sometimes overlaps with Break the Cutie, The Woobie (especially Stoic Woobie), Doomed Moral Victor, With Friends Like These..., and Defector from Decadence. It can even overlap with The McCoy, in which case the character may be a combination of two polar opposites: The Cynic and The Idealist.
"Love is Beneath Me," related to the above - they believe that to be the ones the squad/city/world/universe can depend on, they have to be more powerful and more resolved than the average human being, and above the basest human instincts, especially if they are Badass Normal. See also Love Is a Weakness.
They are maintaining a Secret Identity, and fear exposure if they get too close to anyone. A Cape will frequently combine this reason with the "danger magnet" excuse, and settle for pining for their love interest from afar.
They are asexual and/or aromantic and choose to abstain from any and all sexual/romantic encounters. (Note that it's possible for asexuals and/or aromantics to not have interest in sex/romance but still be open to sex/romance under the right circumstances, so while being asexual/aromantic is not a choice, celibacy is always a conscious decision.)
Rare today is the idea that the heroes' powers rely on their remaining celibate, or that they are celibate out of religious or moral conviction. Most commonly this is found in fantasy settings, which may feature religious orders or mystical powers that may be influenced by sexual activity. Male examples are a rare find in a setting based in the real world, because a man is never, ever a virgin, and don't you dare claim otherwise.
Occasionally, Anti-Hero or villains possessing Power Of Hate cannot afford to be weakened by the thought of having love.
Their religious beliefs demand celibacy. If The Hero is a Good Shepherd, for instance, that would close off any love interest. This will likely come up in the form of temptation. Expect Buddhist (or any other celibate or abstinence associated religion) characters seeking to abstain from physical distractions to fit in here often.
Occasionally a case of a Hero everyone thinks is male actually being female, and pretending to be celibate, asexual or otherwise uninterested in physical relationships (and may be a case of panicking whenever touched at all for this very reason) in order to avoid discovery. You can guarantee that someone is going to try and pounce her anyway, and discover their true identity. If it's an ally, they'll probably be sworn to secrecy. If they're an enemy, you can be assured they'll use it against the Hero, especially if she continues to keep it a secret from her fellow teammates.
By contrast, he may have already fully pledged himself to his One True Love and will not cheat on her with other females, but for various reasons they cannot be together yet (such as having an Engagement Challenge placed on him by his love's family, which is part of the current plot).
Workaholic: This hero doesn't have time for romantic relationships. They're too busy saving the world/patrolling the city/training To Be a Master/etc. This will likely be phrased as being "married to [their] job".
