I need the specific part of the Immigration & Nationality act you are referring?
Also, State Dept Bureau of Consular Affairs:
F. RENUNCIATION FOR MINOR CHILDRENParents cannot renounce U.S. citizenship on behalf of their minor children. Before an oath of renunciation will be administered under Section 349(a)(5) of the INA, a person under the age of eighteen must convince a U.S. diplomatic or consular officer that he/she fully understands the nature and consequences of the oath of renunciation, is not subject to duress or undue influence, and is voluntarily seeking to renounce his/her U.S. citizenship.