What other psychological factors influence self-harm?

Two very common reasons are as follows: (1) If the person feels numb, they may resort to self-harming in order to make themselves "feel" something, and (2) on the flipside, if a person experiences too many negative feelings (depression being the most common), they may resort to self-harm as a means of releasement.

I think bullying and low self-esteem are main factors for that. Also it could be caused by depression, griefing or something similar.

Anxiety, depression, Borderline personality disorder, Bipolar Disorder, OCD, eating disorders, psychosis, depersonalization, mood disorders, personality disorders, body dysphoria, sensory processing disorder ... The list is HUGE (i'm sure there are many more), and, it's possible to self-harm without having a psychiatric disorder. Self harm is a symptom, not a disorder itself, so it can really be related to ANY sort of upsetting emotional state if one find self-injurious behaviors helps them to escape that emotional state. If you feel you may be struggling with a psychiatric illness, it's best to talk to a psychiatrist (who can diagnose you) or a counselor or doctor who can help you find treatment and support.

I think physical punishment as a child can be a influence. As a child, I had the usual "spanking" and hitting for whenever I did something wrong. And at some point in early childhood I recognized this behavior as okay and whenever someone was upset with me, before they could punish me, I would go lock myself in the bathroom and harm myself. Usually banging my head against the wall repeatedly and beating myself senseless. It stopped for a few years but the urge was still there to physically harm myself when I "deserved" it and eventually delved to cutting myself with my nails then knives.

As someone who has self-harmed before it is pain. The need to match the unbearable emotional pain with physical pain. Sometimes I have felt stressed to such a point that I have had to divert my focus in order to get things done. I think pain also plays an important role here. Sometimes both anger and guilt, when it comes crashing down, it seems apt to match that also with physical pain.

I am not sure what "other" means in the context of this question. I doubt that there is a simple answer to it but factors which can but need not be significant include a poor sense of self-worth, abuse (all kinds) during childhood/adolescence and a perception that physical pain is easier to deal with than emotional pain. Obviously all of the above is opinion, not value-judgment.

depression, anxiety, pressure, stress, loneliness, diet, exercise, self care, self-esteem, heart break, lack of support, lack of understanding by others, being overwhelmed with all the above...

Feeling lost, feeling depressed, numbness, prolonged sadness, loss of a close friend or family member, anxiety, frequent panic attacks, etc.

For me, Depression, Anxiety, PTSD and being gay are all interrelated, due to the trauma i sustained at school because of being gay, i am now suffering with depression, anxiety and PTSD. which have played a part in my self destructive behaviour.

Selfharm is often pushed by a sense of control. When life is uncontrollable, at least you have that.