Why?
Article I, Section 1 states "All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives."
Where does it say that the writ can only be suspended through an act of legislation?
Because that is what the Constitution says: powers granted in Article I belong to the legislature.
Where does it say that the writ can only be suspended through an act of legislation? Article I, Section 9 by way of Article I, Section 1.
The same expression, "shall be vested," occurs in other parts of the Constitution in defining the powers of the other coordinate branches of the Government. The first article declares that "all legislative powers herein granted shall be vested in a Congress of the United States." Will it be contended that the legislative power is not absolutely vested? that the words merely refer to some future act, and mean only that the legislative power may hereafter be vested? The second article declares that "the executive power shall be vested in a President of the United States of America." Could Congress vest it in any other person, or is it to await their good pleasure whether it is to vest at all? It is apparent that such a construction, in either case, would be utterly inadmissible."
Justice Jay, Martin v. Hunter's Lessee, 1 Wheat. 304, (1816)