You requested that I tell you why Trump's EO violates the Constitutional rights of Darweesh, Alshawi and other similarly situated lawful immigrants, and I replied that I had already done so, namely that "It violates the Due Process and Equal Protection rights of immigrants such as Darweesh and Alshawi." So what are you asking "Why?" about?
If you are asking why such detention, denial of entry into the US and denial to consult with one's lawyer is a violation of a lawful immigrant's Due Process and Equal Protection rights, it is because those Constitutional provisions are recognized to prohibit such actions by the government, and the Court has recognized these rights for all such persons within the jurisdiction of the US, exactly as Professor Cole pointed out and as I already quoted:
For more than a century, the Court has recognized that the Equal Protection Clause is "universal in [its] application, to all persons within the territorial jurisdiction, without regard to differences of ... nationality."[14] The Court has repeatedly stated that "the Due Process Clause applies to all 'persons' within the United States, including aliens, whether their presence here is lawful, unlawful, temporary, or permanent."[15]
http://scholarship.law.georgetown.edu/cgi/viewcontent.cgi?article=1302&context=facpub
The cases cited in these two footnotes are
Yick Wo v. Hopkins, 118 U.S. 356, 369 (1886),
Zadvydas v. Davis, 533 U.S. 678, 693 (2001), and
Mathews v. Diaz, 426 U.S. 67, 80 (1976), "holding that due process applies to all aliens in the United States, even those whose presence is 'unlawful, involuntary, or transitory'".
These facts are the basis for judge Donnelly's stay of the EO.