The Constitution is absolutely silent on who specifically can suspend habeas corpus, but that doesn't stop your cohort from stating that since Congess is mentioned in Section 1 then the implication is that Section 9 applies only to Congress as well. Why are implied powers OK there and not OK in Article IV? Other than the fact that one fits your purposes and one does not, of course.
WRONG. The power to suspend is the writ is listed in Article I, prefaced by, '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.'
'All' as in ALL powers. 'Legislative' powers, not Executive nor Judicial, not shared. 'Shall be vested' in Congress, not the President. 'Herein' granted, as in this Article.
Article II states, 'The executive Power shall be vested in a President'. No mention of suspending the writ. Same for all other Articles.
Chief Justice John Mashall thought so when he wrote, 'If at any time the public safety should require the suspension of the powers vested by this act in the courts of the United States, it is for the legislature to say so. A decision of the US Supreme Court. Just as Chief Justice Taney thought it was for the legislature to decide when he wrote that it was, 'one of those points of constitutional law upon which there is no difference of opinion, and that it was admitted on all hands that the privilege of the writ could not be suspended except by act of Congress.'