Why do I feel so awkward when someone refuses a present from me?

[Der/die AtheistIn]

Depends on the culture and your relationship with the giver.  Eg In Japan, one bows politely ,says thank you, and opens the gift later, in private. Japanese society has a complex system of reciprocal gift giving, as well as things it is impolite to give...... Just hope you never become involved, it can be a nightmare.

here in Oz, I was taught that the minimal polite response is "thank you".

"You shouldn't have" is false modesty and disrespects and often annoys the giver. To refuse a gift is churlish.

In my country there is often an implicit reciprocity with gifts, especially with family.

Gae Bolga  is right I think; each country has its own customs of reciprocity, whether in goods or favours* .This often seems unrelated to Christian
values.

Think of Don Corleone's 'favours'.  Real life is a lot like that, differing only by degree.

In my country it's tradition to reject the present at first a few times, then at the end to accept it. It's considered impolite to accept it right away.
However, this tradition is dying.
As a kid I didn't follow it, as an adult I do when talking with people from my country, though sometimes they won't insist, which makes me confused to which tradition to follow.