So ‘but’ is not necessary? why? I agree with Amy that ‘but’ is a conjunction in this case, and so without ‘but’ we have 2 sentences (‘I’m sorry’ and ‘I have to finish my term paper today’) with no link? It’s wrong, isn’t it?
I would recommend always including the word ‘but’, especially in more formal English.
It can be omitted in informal English. However, excluding it does tend to make the sentence sound more abrupt, and therefore not as nice/polite, in my opinion.
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