Given the following sentence, am I correct to input the word "worse" to fill in the blank and make the sentence understandable?
I cannot speak Chinese very well, and he cannot either.
His Chinese is no __ than mine.
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You would say “better”, not “worse”.
It has to do with the contrast between the idea of speaking Chinese “very well”, and the two of you not being very good at it.
You state that you cannot speak Chinese very well, and then introduce your friend’s ability. To get to “very well”, from where your skill level is, you would need to get better. Can your friend’s skill level provide a surrogate for this betterment? No, because:
His Chinese is no better than mine.
The implication being that if his Chinese were better than yours, then, yes, maybe it could.