Is my rejection of gifts from relatives and neighbors, out of fear of obligation or reproach, considered arrogance or haram, especially since I have enough for my present and future needs, and my family has its own income?

There is no harm in not accepting a gift, because it is not obligatory, nor is rejecting it forbidden. This is particularly true when there is fear of obligation, reproach, or boasting on the part of the giver. It is permissible to reject a gift for reasons such as the giver not being content with the usual reward, or if the gift is given after being requested, or to avoid obligation. Sometimes, rejection may be obligatory, such as refusing a hunting gift from someone in a state of ihram (definition). This is not considered arrogance, as arrogance is defined as rejecting the truth and belittling people.