The Declaration of Independence is the document with that ringing phrase (inalienable rights), but that is not the governing document of the United States of America.
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The inalienable/unalienable word is not there (constitution)because the constitution spells out restrictions on the government's rightful ability to alienate a person from their rights.
IMO Beechhouse makes an excellent point. It is obviously true that The declaration of Independence and the Constitution are quite different documents, written at different times, with differing intents, and differing governing authority.
The Declaration was a document written absent all significant concerns of governance. It's sole intent was to provide a basis for separation from an authoritarian government. The declaration is inspirational; revolutionary in nature. It has no governing authority. And so it is no surprise that the Declaration would drastically narrow that valid scope of government and emphasize individual rights that are the basis of revolution against an existing government.
The people writing the constitution faced a quite different challenge. They had to figure out how to actually govern the nation now free of oppression. Having that challenge, they realized that individual rights and government power had to be balanced in a way that prevented the government from crushing individual rights but still gave government sufficient power to achieve the legitimate aims of government (what ever they are). And so it is that in the governing document (the constitution) there is no discussion of inalienable rights. Instead there is a detailed discussion about the limitations of government's power to alienate the rights of individuals and states.
