Trade winds and Age of Sail routing

Why do Aubrey-Maturin sailing passages cross the Atlantic before heading for the Cape of Good Hope instead of staying near Africa?

Trade winds and tides could make a double Atlantic crossing faster than the shorter-looking route down the African coast.

Age of Sail routing followed wind and tide, so the fastest passage could look indirect on a modern map. An Aubrey-Maturin voyage might cross toward South America before turning for the Cape of Good Hope because the trade winds made that route quicker. Predictable wind routes also concentrated ships in recurring interception zones. Ushant and Trafalgar are cited as examples of battles occurring where sailing conditions carried fleets and allowed enemies to wait for them.