Youre comparing apples to oranges.

Animals and plants have completely different systems evolved for dealing with things like infection and pests or parasites. Right down to cell structure.

Many plants have evolved such that a broken branch can heal to become its own entire plant (a genetic clone of the original) and a lot of that is down to cell structure and how relatively simple a plant is in operation.

Compared to how varied animals are; we span every environment to some degree, we consume a huge variety of food (which puts us at risk of as many different infections and parasites as you can imagine) we exist in various states of health for extended periods of time, and we have differing aspects of health (i.e. a tree needs sun, air, and water. We have dietary needs far more complex, we have mental health that can and does have physical implications) so for humans/animals, we evolved an immune system specifically for the purpose of handling many of these issues. And the issues are so varied, the immune system must make a distinction between the body its trying to protect and foreign material - else it cant do what needs to be done (the person dies due to a lack of effective immune system) or the opposite extreme where the immune system doesnt properly make the distinction between friend and foe; known as an autoimmune disease where it attacks tissues its supposed to protect. This is why it attacks another humans tissue. That tissue could carry disease or parasites, it isnt the tissue its programmed to protect. And the immune system has evolved successfully by attacking these things.

Animals and plants are very, very different.