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inhuman
1 b : cold, impersonal <his usual quiet, almost inhuman courtesy - F. Tennyson Jesse>
[M-W's Col. Dic.]

Counrtest by its very definition is an humane act. Then, what would be an "inhuman courtesy". Suppose, there is an accident. A child is ran over. The guilty rich driver of the car pay a huge sum of money to the mother of that child only to save himself from law and has no care or sorrow for what he has done. I won't call 'compensation money' an act of courtesy.
Comments  
Inhuman (not inhumane) courtesy-- Overly courteous; more courtesy than we could reasonably expect from a person.
inhuman
1 b : cold, impersonal <his usual quiet, almost inhuman courtesy - F. Tennyson Jesse>
[M-W's Col. Dic.]

Neither the definition nor the example phrase suggest anything such as 'overly courteous'. 'cold' commonly suggests lack of emotion and has negative connotations in such contexts. So, please help me to know where I'm going wrong in my interpretation. Thanks.
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Over-politeness has a cold aloofness about it.
Please don't mind my asking again. Could you please explain it a little bit, how can 'over-politeness' have cold aloofness about it? 'over-politeness' is a good thing, isn't it?
No, it is not. The appropriate amount of politeness is a good thing. Under and over are not.
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I have just noticed that you have changed your profile picture. Your previous picture I think was more relevant - an English Guru. Is it just a random new picture, or does it have any meaning to it?

I find a poor, ragged person on a road in a very bad condition. I give his lift in my car, take him to buy new clothes, give him something to eat, and also offer him some monetary help so that he can get settled. He can return the money once he has a job. Would it be over-politeness? In what way would it be a bad thing?
None of that is courtesy. It is all kindness. Continually calling the ragged person 'sir' would be overly polite and perhaps not taken so well, but as patronizing.