I'm beating on port and the boat just to leeward wants to tack but can't tack into me, so she shouts "Please tack!" — do I have to?

No. No rule makes a windward boat tack because she's asked. A "Room to tack" hail under Rule 20.1 only works when the hailing boat is approaching an obstruction, and wanting to tack isn't one. You can hold your course. But the leeward boat isn't stuck: under Rule 11 you must keep clear of her, so she can luff you, right up to head to wind, as long as Rule 16.1 gives you room to keep clear.

📖 Want more situations like this one? Bryan Willis's The Rules in Practice 2025-2028 works through the rules as they happen round the racecourse. (affiliate link)

▶ Watch on YouTube ↓ Download (via YouTube)
<iframe width="560" height="315" src="https://www.youtube.com/embed/WT9uGo8MjdE" title="Sailing Kiwi" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
<p><a href="https://sailing.kiwi.nz/v/WT9uGo8MjdE/">Source: Sailing Kiwi</a></p>

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Next on this shelf — The Upwind Beat