Trigger warning: ableism, murder, something that's kind of like silencing
No one is normal, no one conforms exactly to what society has, why can't we all get along, why do we all feel the need to change people? On one hand, I want all these things. I want to be able to get along, I want there not to be a need to change people. But I know why these things are there.
It is true that there is no normal that truly exists, that it is just a construct by society. There is no one "normal" person, never was, never will be. So many of us are more comfortable with people like ourselves that we take as normal those with a certain amount of similarity to ourselves, and if we have sufficient power in society, this normal may override the normals of others. Power, privilege, oppression. There is no normal. There are privileged identities and disprivileged ones, and the disprivileged ones come with varying difficulties and varying levels of possibility for either joining the privileged group or for hiding the fact that you are not a member.
I can not really pass for neurotypical. I certainly don't pass for male. I do pass for binary and cis, though as my identity is androgyne, I am neither of these things. I am able-bodied. Though I am occasionally mistaken otherwise, I am white. I have received a good education, and I am still receiving education. I can read. I can write. I can type.
Some of these things are considered "normal," and some aren't. Some are things that you would never mention when you describe me, but which you would mention if you were describing someone who didn't have that trait. That is a sign that the trait is considered normal, that it is the privileged trait.
Neurotypicality is privileged over neurodivergence. Able-bodiedness is privileged over physical disability. Maleness is privileged. Binary genders are privileged. Whiteness is privileged. Being able to speak the dominant (privileged) language of an area is privileged. Literacy is privileged. Normalcy often seems to read as "has at least X privileged traits, including a certain set of them." Neurotypicality and able-bodiedness are usually on the must-have list, though passing is sometimes enough and huge achievements a la Stephen Hawking can earn an exception.
When you tell me there is no such thing as normal, this is true, in a sense. The things we as a society prize as normal can not all be found in one person. But there is privilege, and there is power, and some people are closer than others. Remember, when an Autistic person is killed by a caretaker or parent, it is viewed as being about the caretaker snapping and the murderer gets sympathy. When we are killed for the way that we are not normal, few decry this. That's how it's different than just being a little weird.
Don't use the fact that no one is actually quite normal to invalidate the fact that being further from it in certain ways leads to actual institutional oppression. If you do, you are contributing to that oppression, and there is blood on your hands.