The person who gives you time to finish deciding has protected the quality of your answer.

Rushed decisions are usually worse decisions, and the rush often comes from the person waiting rather than from the thing itself. With somebody standing over you, you start optimizing for ending the discomfort, which is a different task from choosing well. Anyone who says take your time has quietly improved the answer you will give. It costs them patience and buys you accuracy.

When you want an answer from somebody, give a real deadline and then stop pushing. When you are the one deciding, ask for the time you need instead of hoping it appears.