The person offering to pick something up is lending you part of a journey they already planned.

Some help costs almost nothing to give and a great deal to do without. When someone is already going to the shop, adding your item is a small extension of a trip that was happening anyway, which is why the offer is easy for them and genuinely valuable to you. People often refuse this kind of help out of a wish not to impose. The imposition is usually far smaller than the refusal assumes.

Say yes the next time such an offer comes, and name something specific rather than deflecting. And when your own errands are set, tell one person where you are going.