I want to know why a woman feels something odd when a male stares at them. I have tried this on many girls. Some feel irritated , some became angry, and some even leave the room.
I don't think you need to resort to hormonal or neural explanations. Staring has social meaning. The meaning of staring varies across cultures and contexts. In some contexts it is normal (e.g., staring at a presenter, staring at the person you are talking to, staring at a sales assistant). In these contexts, staring has meaning such as indicating interest or indicating an accepted attempt at engaging the person's attention.
In other settings staring can violate social norms and may be interpreted as an aggressive or annoying action by others. In some cases, staring can make people feel self-conscious or objectified. In other cases, a stranger staring at them can be experienced by the person being looked at as an intimidating action.
You can imagine a train of reasoning that might arise when you stare at a women long enough for her to notice and for you to notice that she has noticed. She could be thinking that she doesn't want to be stared at and that social norms say that she should not have to be stared at. Yet, you continue to stare at her. At the very least she might find this disrespectful. In some contexts, it might induce concern that if you are willing to break that social convention, you might be likely to break others, which give rise to fear that you might be violent. In other contexts it might just be interpreted as a sexual advance, which they don't want to reciprocate.
Anyway, the main point is that staring has complex social meaning, and thus should be understood within the social context including prevailing norms about staring in general.
It seems that the academic Rosemarie Garland-Thomson has written quite a bit about the meaning of staring from a humanities perspective.
See for example, her 2006 article
This article considers how staring informs the ways we know each other and the world around us. Staring, a complex, nuanced, and meaning-laden social interaction, can take many forms: arrested, separated, or engaged. It is an intense encounter which is sometimes a random, idiosyncratic confrontation and at other times a highly structured social ritual driven by the collective impulse to look. This article argues that staring often defines the relationship between disabled and nondisabled individuals. More important, however, it seeks to redefine this relationship by imagining, perhaps counterintuitively, the object of the stare as determining the structure and outcome of the staring engagement. The staree may take charge of the encounter, in other words, using various strategies to both mediate and transform discomforting interaction into an unexpected opportunity for mutual transformation.
Or her 2005 article
Staring is a vivid form of human communication. Part of our enormous communal vocabulary of the eyes, staring is a particularly emphatic way of expressing our response to others. A more forceful and sustained form of looking than glancing, glimpsing, scanning, contemplating, surveying, gazing, and other forms of casual or normative looking, staring starkly registers intense interest and endows it with meaning. That interest ranges widely in form--from domination, adoration, curiosity, surprise, allegiance, disgust, wonder, befuddlement, openness, hostility, to reverence. The stare is a highly charged interpersonal encounter that we snap up in a variety of contexts to put a sharp point on what we mean, think, or want. Staring is a way of strongly reacting to another; it bespeaks involvement. It is the human response to novelty, to the unexpected.
As such, staring is an embodied and relational visual exchange that carries complex cultural and historical meanings. Like sex and eating, staring is drenched with significances, scrupulously regulated, and intricately ritualized. Civility, for example, has always strictly governed staring and prescribed what we do with our eyes in social encounters. In American culture, the one thing everyone knows about staring is that your mother told you not to do it. Both furtive and compelling, staring is imagined as a formidable interchange and is a source of vivid narrative within in the Western cultural archive.
She even has a book called Staring: How We Look. Oxford University Press, 2009. She talks about the book in this short YouTube clip.
