Why the possibility of Jang Mi-ran's death being a homicide is much higher

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First, statistically speaking, hanging usually results in asphyxiation rather than a broken neck.
The probability of a fracture is higher in the elderly, males, or those with heavy body weight.
Furthermore, in cases of incomplete suspension where part of the body touches the ground, as in the case of Jang Mi-ran, the probability of a fracture drops significantly.
Looking at domestic and international data, the occurrence of cervical spine dislocation in hanging is estimated to be between approximately 15% and a maximum of 40%, while French data puts it at a mere 1-3%. This inevitably relates to the structural layout of the house, such as ceiling height. If the ceiling is high, like in the US, it is conducive to suicide.
If one considers suicide with minimal pain, the cervical spine must be broken. That is the only way to ensure instant death, but as seen in the hesitation marks of those who commit suicide using knives, it is difficult unless one is extremely bold. People know that severing the carotid artery would end it easily, but they fail because they are too afraid and only fumble with their wrists.
The most effective method would be to wrap a rope around the neck and bungee jump off a building, as seen in the movie Omen. Of course, while this satisfies the first principle of suicide—minimizing pain—it violates the second principle of minimizing the shock to family and onlookers. One cannot satisfy everyone when they are in the process of dying.