Differences in Declining（拒绝） an Invitation

Declining（拒绝） an Invitation differs between China and the West.
Most people in the west don't like to give detailed explanations（细致的解释） Their explanations are usually short and simple, such as " I’m sorry, I can’t get away （拖不开身）" or “ I’m tied up（非常累） the whole week” or “ I'm already busy that night." 
But in China, people will give a more detailed explanation（细致的解释） , then the person making the invitation will understand there is something important. 
So, the Chinese detailed explanation（细致的解释） sounds unnecessary to the Westerner, and the Westerner's short, un-detailed explanation(不细致的解释) sounds impolite（不礼貌的） to the Chinese.