Read these two paragraphs very slowly and then please quote where it says us does not recognize dual citizenship.
Dual Nationality
U.S. law does not mention dual nationality or require a person to choose one nationality or another. A U.S. citizen may naturalize in a foreign state without any risk to his or her U.S. citizenship. However, persons who acquire a foreign nationality after age 18 by applying for it may relinquish their U.S. nationality if they wish to do so. In order to relinquish U.S. nationality by virtue of naturalization as a citizen of a foreign state, the law requires that the person must apply for the foreign nationality voluntarily and with the intention to relinquish U.S. nationality. Intent may be shown by the person’s statements and conduct.
Dual nationals owe allegiance to both the United States and the foreign country. They are required to obey the laws of both countries, and either country has the right to enforce its laws. It is important to note the problems attendant to dual nationality. Claims of other countries upon U.S. dual-nationals often place them in situations where their obligations to one country are in conflict with the laws of the other. In addition, their dual nationality may hamper efforts of the U.S. Government to provide consular protection to them when they are abroad, especially when they are in the country of their second nationality.