Yes - you have CD8 and CD4 T cells apart from the B cells that make antibodies. These adaptive immune cells routinely react to self-antigen and are then destroyed for doing so. Auto-immunity usually results from a failure of this filtering.

Usually in auto-immunity the CD4 cells coordinate a CD8 and B cell response to self-antigen, so the antibodies aren't super necessary. Theoretically, you could have an autoimmune reaction without self-reactive antibodies, but this would be uncommon.

Neutrophils are part of the innate immune system, which is rarely self reactive because its behaviour is genetically defined.

Can neutrophils decide to be autoimmune?

No, because they don't have adaptive receptors targeted towards self antigens.

It is important not to confuse autoinflammitory with autoimmunity. Autoimmunity is based on either T-cells or B-cells (or plasma cells which are derived from B-cells) having their characteristic adaptive receptor (B cell receptor or T cell receptor) strongly bind to specific self antigens.

Note that T-cell autoimmune diseases are still hypothetical.

(More specifically, no one has characterised the T-cell receptor repertoire and demonstrated close to 100% sensitivity or specificity for a T-cell receptor subset for any disease - anyone claiming I am wrong is going to have trouble citing proof). T-cells undergo a strong selection process in the thymus to prevent autoimmunity, whereas no such process occurs for B-cells. B-cell autoimmunity doesn't necessarily need T-cell autoimmunity either.

Whereas all currently well-characterised autoimmune diseases are either B-cell diseases (associated with autoantibodies) or are in fact autoinflammatory, rather than autoimmune diseases. For example the Arthropathies do involve self-reactive T-cells but this self reactivity isn't primary driven due to self-reactive T-cell receptors, but rather they are causing inflammation regardless of what the T-cell receptor codes for.

There are parenoplastic diseases (T-cell cancers) that can rarely be autoreactive but these are extremely rare and the primary disease is the cancer.

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Autoantibodies are like markers for autoimmune diseases, but can other things like white blood cells cause autoimmune diseases too?

From what I've learned, it turns out that autoimmune diseases can happen without autoantibodies. Some diseases are caused by other parts of the immune system like T cells, B cells and not just autoantibodies. And specifically about neutrophils, they are a type of white blood cells and play an important role in fighting infections but it's not clear if they are involved in autoimmune diseases.

It's all pretty confusing, but it seems like autoimmune diseases can have different underlying causes. So, it's possible that some autoimmune diseases can happen without autoantibodies.

Well, how i understand it currently, the T-cells need to recognise the antigene or antibody of a virus or cell first to attack them, they can find these antigenes and antibodies themselfs, or they can be presented to them by another cell.

So if the T-cell has a mutation and decides one of your cells antigene means trouble, they will attack. But that is just 1 cell, so it wont cause an autoimmune disease. That can also happen from overpresentation (for example if you have a little to many bacteria in your microbiome), wich is when it CAN cause an autoimmune disease, because its a lot of cells that go against you.