Sometimes, it's society itself. In stories where there are strict social norms about who can love whom, like in some historical or cultural settings where interracial or same - sex love was not accepted. Society with its prejudices and laws acts as the antagonist, making it difficult for the lovers to be together.
They are often manipulative. The antagonist might use lies or schemes to break up the couple. They could spread false rumors about one of the lovers to make the other lose trust. For example, in some stories, an envious character may tell the girl that the boy has been unfaithful when it's not true, just to drive them apart.
Well, in many love stories, the antagonist may have a strong sense of entitlement. They think they deserve the love of one of the main characters more than the other person in the relationship. This can lead them to engage in all sorts of devious actions, like spreading false rumors about one of the lovers to break them apart. They might also be controlling, trying to manipulate the situation to their advantage so that they can get what they want, which is usually the affection of one of the protagonists.
It depends on the specific story. Different stories have different antagonists. Sometimes it could be a villain with evil intentions, and other times it might be a character with opposing goals to the protagonist.
An antagonist is basically a character or a force that opposes the main character or protagonist. They create conflicts and obstacles for the hero to overcome.