If an attacker learns a pseudorandom generator's seed and algorithm after watching several outputs, why can the later outputs become reconstructable?

Answer: The sequence is deterministic

The sequence is deterministic ✓ — A pseudorandom generator is a recipe, not a new coin flip each time. With the same seed and algorithm parameters, the same sequence can be recreated, even if its early outputs looked patternless. Cryptographic generators are judged by a stricter goal: without the secret inputs, previous outputs should not let you predict the next one.

Outputs add fresh entropy — Watching outputs does not add new entropy to a deterministic generator. The sequence may feel refreshed because more values have appeared, but those values are still consequences of the same seed and algorithm. Once those starting inputs are known, the later values can be replayed rather than newly discovered.

Balanced bits hide state — Balanced bits can hide obvious visual patterns, but they do not hide the internal state once the seed and algorithm are exposed. A stream can have nearly equal 0s and 1s while still being completely reproducible. Security depends on unknown state, not on the output merely looking evenly mixed.