Jesus Christ asks us to deny ourselves but not to deny Him. Many have died at the hands of others because they refused to deny Jesus as Lord and Savior. This has even happened quite recently in the Middle East, where Christians, children even, have been murdered by Muslims because they were asked to reject Christ and submit to Islam and Allah and they refused. The latest I believe were the Coptic Christians in Egypt on that bus who were slaughtered in the name of Allah and Mohammed.