For the cat, staring at another cat or person is essentially an aggressive act. Although I think you have to also take into account the circumstances as it won’t always be aggressive, far from it. For instance I often stare at my cat and he stares back but we are father and son so it is allowed!
If there are a group of people in a room who are strangers to a cat who enters, it is possible that the cat will approach the person who is the most fearful of domestic cats while avoiding those who love them. This is not a scientific formula but the scenario may play out as described.
The person who is fearful of cats will tend not look at the cat as he or she enters the room. They avert their gaze whereas the cat lovers look intently at the cat in interest. They like cats and want to look and engage.
The cat who rubs up against the cat hating individual is not being deliberately clever and irritating. They believe that the person is non-hostile and therefore friendly because they did not stare at them. Conversely, the cat lovers who stared are regarded as a hostile. These people are avoided.
The end result is the exact opposite to what should have happened. The cat should be attracted to cat lovers. The answer then, in order to attract a strange cat, is to be immobile and not stare. The person is not demonstrating intimidating body language towards the cat. This is broadly inline with Jackson Galaxy’s advice in meeting new cats. He says you should be passive and use the Michelangelo finger greeting.
If you want to avoid a cat coming towards you, Desmond Morris says that people should “stare fixedly at it with wide-open eyes and make agitated hand movements, asking the cat in strident tones to come and sit on their lap. This will have exactly the opposite effect and the persons will then be able to relax without appearing to have insulted their host’s favourite pet”.
The cat’s owner is exempt from this rule because they are pseudo-mothers and allowed to stare at their “kitten” because they are expected to be concerned about their kitten’s welfare.