" makes sense, and might be used, but the given answer seems better in typical situations. "he will have been on holiday next week" isn't right. "will have been" is used to look back from a projected point in the future.
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rpshWill you be seeing **** at the meeting?The progressive form of "see" almost always has the meaning of "meeting with, talking with."
rpshNo, he will be on holiday next week.The simple future is correct here.