I cannot do it alone, but neither can you.
Question: Is it okay to use the conjunction “and” instead of “but” here?
So the sentence would be like “I cannot do it alone, and neither can you.”
Thank you!!!
Yes 
You could use “and” but there’s a subtle difference. If someone says, “I cannot do it alone and neither can you,” this places the speaker and the other person in the same position. They both cannot do X alone. This is something they share; they both need another person. Depending on the tone of voice, it could be a casual observation.
However, if someone says, "I cannot do it alone BUT neither can you! " this emphasizes that the other person cannot do X. alone. It is a stronger statement which, judging from the facial expression on the girl, is what I am guessing she wants to convey. to her boyfriend (?). She is emphasizing that HE cannot do it alone (without her?). That’s the main point, that HE cannot do something by himself. (Did he want to?)
I don’t know what went on in the dialogue previously but I am guessing that it’s not a friendly discussion about each other’s abilities but instead is an argument. That is why “but” is the more obvious choice in this situation.
Again, I am surmising the scene from the body language of the characters. Context would affect whether “and” or “but” is
the more likely conjunction in the dialogue. The issue is not what is grammatically correct but which conveys the desired emotional impact .
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