If you stifle your natural feelings or behaviour, you prevent yourself from having those feelings or behaving in that way. It is best to stifle curiosity and leave birds' nests alone = suppress
{f} hold back, restrain; crush, quell; smother, suffocate, asphyxiate; be suffocated
impair the respiration of or obstruct the air passage of; "The foul air was slowly suffocating the children"
To suppress the manifestation or report of; to smother; to conceal from public knowledge; as, to stifle a story; to stifle passion
To stop the breath of by crowding something into the windpipe, or introducing an irrespirable substance into the lungs; to choke; to suffocate; to cause the death of by such means; as, to stifle one with smoke or dust