Users follow other users and see a merged, reverse-chronological feed. The whole design turns on one decision: when is a feed assembled?
Fan-out on write pushes each new post into every follower's precomputed feed. Reads become a single lookup — extremely fast — and writes become expensive in proportion to follower count. A post from an account with 50 million followers is 50 million writes.
Fan-out on read stores posts once and merges at request time. Writes are trivial, reads are expensive, and the cost falls on the operation you perform far more often.
Real systems do both: fan-out on write for ordinary accounts, fan-out on read for the handful of enormous ones, merged at request time. That hybrid exists because neither pure strategy survives the follower distribution, which is heavily skewed.
You start with a single database serving reads directly. At 30,000 feed loads per second it does not stand a chance.