What Fallacy Is This?--That's Not Important
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Original Question
A makes an argument for claim X
B responds: I don't think what's important is X. What's important is that...Y.
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B's response is both dismissive of A and an attempt to change the subject.
Comments on Question
Answers
1It seems like a case of people talking past each other, because they have different goals.
So if this were a debate about COVID-19 measures, for instance, person A could be advocating for a lockdown, citing the need to 'save lives'. Person B could be advocating against lockdowns, citing the need to 'preserve the economy'.
If person A presented their argument, it'd be fine for person B to explain why their goal is more important...as long as they explain why. As in, it would still have to be a counter to the original argument - either accepting that X is important, but less so than Y, or demonstrating that X actually isn't all that important. This way, both people in the conversation could advance different goals while still responding to one another - talking to, rather than past, each other. If they didn't, and simply tried to avoid the subject, this would fall under red herring.
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Well, yes, your conclusion does have validity, but it can also be a statement of different sets of values that A & B has. A may claim that X is important because it is central to their personal value system. B, on the other hand, may have an altogether set of values and dismiss X as being important and instead lay claim to Y as being important instead. So it may not necessarily be a fallacy, but a manifestation of opposing value systems play. At least that is my 2 cents worth.