commonly normality is equated with being able to "fit in", which in turn gets interpreted as being similar or being the same as most, not being different or original, not having traits that would make stand out. i find that to be either inaccurate or incomplete understanding of phenomenon of normality and what normality is and isn't; i think that's best portrayed in analysis of what being "abnormal" is and why - and how - it exists as a concept.
being abnormal means defiance, but specifically defiance that alienates, unique character that separates, differences that creates distance. being abnormal is to have a level of separation between yourself and other people or wider society, a "wall" which makes intimate, direct communication difficult or impossible, having problems connecting with other people and participating in group life. obviously, all people are different, multiple have outstanding or characteristic traits and personalities - i.e. "bubbly" people, childish people, quiet and shy people, loud people, on the other end men who have anger issues, and a lot of characteristic traits, even found rarely in the population, aren't understood as "abnormal". abnormality does not boil down to being "different" or even "different in a rare way". abnormality only refers to only not living, not thinking or not acting like most in a way that alienates and makes connecting with others difficult of impossible. people capable of connection who are not alienated, no matter how much different they are from the average joe, will not fall into the "abnormal" category, because it's not a category of "similar vs different", it's a category of "these who are alienated and exists on the margin vs these who aren't".
differences that don't alienate exist as tolerated variation within normal bounds: being abnormal is unavailable for connection, excluded from the community.
it's not being able to communicate on the same "frequency", relate and be related to and be understood, it's frequently being misinterpreted - like autistic people.
it's not being able to participate in the same activities and share the same lifestyle - like physically disabled people.
it's inability to share the same cultural codes, the same formative experiences growing up, being excluded from conversations about boys or girls in high school, from relating on sexual life and capability of creating a nuclear family - like gay men and lesbians.
t's having experiences, processing and emotionality which aren't relatable and understandable to most, and which therefore seem alien and unpredictable - like mentally ill people.
of course, it's related to the theory that states "functionality" according to societal, capitalist standard is the criterion which separates normal from abnormal, but that too is an incomplete understanding of the phenomenon - lack of functionality is condemned due to failing to participate in building capital, but a lot of people branded abnormal are capable of meeting the capitalist standard of "contribution" or "functionality", such as working or maintaining a household. at the core, though, meeting the capitalist standard set for a member of society requires identifying with the society, local community, nation and other structures based on net of connections, and it can only be suspected a person who is alienated - not necessarily completely lonely, but alienated from most - will not feel much of a connection to these structures nor willingness to sacrifice their health and life for them, and is likely to reject these structures, not have much stake in them, and be pushed away.
being a participant of constructs such as the nation requires having solidarity and a sense of community and connection with a bunch of other people, often strangers or otherwise not freely chosen, and thus not feeling alienated from most, and not being alienated by others in ways that make being part of such a construct and finding a productive role within it difficult or impossible because of being misuderstood, encountering distrust and suspicion et cetera, which renders one basically unable to participate in them in the "right" way, be it by their own aggressive, depressive or withdrawn depression or due to ostracism; or they're incapable of participating in a way that isn't shallow or undermining the constructs' principle; and a person like that is likely to not care about the society they largely cannot connect to, feel alienated and rejected by, and due to not caring is not willing to make sacrifices on the altar of that constructs - sacrifices necessary for the higher class exploiting the construct to benefit, and sacrifices lack of which encourages other members to also slack on what is considered their obligations and duties as well as their expected default. since they cannot connect with the average person and most of their surroundings, they will not identify with and play their role within structures correctly.
a "functional" abnormal person is still a threat, since they may use their position to neglect contribution to the construct or sabtotage it from the inside; since they are alienated, the state, society or whatever else can't count on their loyalty - it's unlikely that they would feel a parasocial love (what i consider attachment to constructs such as the nation) and identification if they are alienated. they do not relate or identify themselves with what they can't connect with, they have little reason to care or to exhibit loyalty and solidarity, and they don't have much to lose; so sooner or later they will threaten the structure they cannot relate to and cannot find a place in. on account of that, it's best from the point of view of the ruling classes to separate them or destroy them, or install in place mechanisms which would prevent the more "functional" ones from getting too much power and responsibility which they would probably use for their own interests or worse, to deconstruct and change the structures they don't belong to.
worth noting, there's people who are perceived as "normal" despite being notably abnormal i.e. mentally ill, while some, even functional, will never be perceived that way; it's a matter of ability of connecting to the average person and being included in social structures, such inclusion creates illusion of normality for the outsiders, who only see the connection and inclusion, while the people in question may still feel alienated, experiencing responses and processing they can't see in most people around them and being forced to hide a part of themselves; then their alienation is solely internal, so they "pass as" normal on account of not being alienated in a way that's visible and interrupts entering connection with individuals and groups who don't suffer from any form of alienation.
my conclusion in general is that it's not existing outside of the norm that causes alienation, it's alienation that causes being being relegated to the category of "abnormal".
"normality" in itself is somewhat of a construct of capitalist and patriarchal society as is; "normality" refers to being part of the structures on which the whole system rests on - structures such as the peer group, family, especially nuclear family, or mentioned nation, or community of people of the same sex, et cetera. "abnormality" consequently means disconnection which, due to being exlcuded from these structures, causes existence on the margin, outside of these structures, which inevitably means being a threat to these structures or at very least completely useless to them in terms of exploitation.
this isn't meant to imply it's people's "fault" that they're seen as "abnormal" or that it's inherent and unchangeable because they cannot connect with the average person and, usually, most of their surroundings; i am very far from victim blaming in this regard, especially as a person very strongly stigmatised as abnormal most of my life, and very alienated in most structures i was obligated to be part of. if "abnormality" wasn't identified and contained as a category and wasn't condemned and attached a negative character to, it'd be possible to deconstruct it. essentially what i mean is that if the majority reached out and learnt more about the groups they exclude and the people they cannot understand, and if these groups didn't hold understandable grudges for the horrible treatment they received, connection would most likely be possible; it's just that connection in these cases of fewer shared experiences and languages of communication takes active effort to get to know each other and an open mind and willingness to do so, which is not going to happen when the category of abnormality exists, is negatively marked and immediately attached to those who cannot connect to the social structures they find themselves in.
i suppose this is that on normality, and what i call the hypothesis of alienation, which in short bases itself on the notion that normal = wired into a net of social connection which keep them engaged in the constructed society, while abnormal = alienated and thus likely to be a threat to these constructs by fighting them externally, questioning them or undermining them internally by participating in them "wrong".