Spread Spectrum needs synchronized despreading which can be degraded by multipath effects.
OFDM relies on orthogonality of subcarriers, and the frequency drifts will offset the orthogonality. Multipath effects will not hurt OFDM, because they do not change frequency.
extended reading: Sec 2-3-1-d & Sec 2-3-1-e of Textbook
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