The question really isn't a "double standard", per se, but a question of if a successive President can drop something from a prior administration
For - It was done improperly without justification
The problem SCOTUS had here is that the Trump administration provided no legal reasoning for rescinding the program
In the case of DACA, Attorney General Jeff Sessions announced on September 5, 2017, that the rescission was necessary because DACA had been created by the Obama administration “without proper statutory authority,” and thus constituted “an unconstitutional exercise of authority by the executive branch.”
There were, and are, respectable arguments to be made that he was right. But the fact is, Sessions didn’t bother to make them. And when Acting Homeland Security Secretary Elaine Duke followed up with an order winding down DACA, she didn’t either.
Where the Administrative Procedures Act(APA) comes into play is
In the litigation that followed, the administration’s approach was “We don’t got to show you no stinking reasons.” These questions were, in the words of the Administrative Procedure Act (APA), “committed to agency discretion by law,” and thus no business of judges.
The [then Attorney General] Sessions memo and the rescission memos, [Chief Justice] Roberts then wrote, did not come close to fulfilling the APA’s procedures: “DHS was ‘required to assess whether there were reliance interests, determine whether they were significant, and weigh any such interests against competing policy concerns,’” Roberts wrote. The agency did not even pretend to do that.
The argument is that the Trump administration rushed into this and crafted law that needs an argument for why it was removed. The courts didn't strike it down on substance, only procedure.
Against - This will open up lots of legal challenges of executive order rescinding
This was noted by Justice Thomas in his dissent (starts on page 39 of the SCOTUS decision)
At bottom, of course, none of this matters, because DHS did provide a sufficient explanation for its action. DHS’ statement that DACA was ultra vires was more than suffi-cient to justify its rescission. By requiring more, the majority has distorted the APA review process beyond recognition, further burdening all future attempts to rescind unlawful programs. Plaintiffs frequently bring successful challenges to agency actions by arguing that the agency has impermissibly dressed up a legislative rule as a policy statement and must comply with the relevant procedures before functionally binding regulated parties. But going forward, when a rescinding agency inherits an invalid legislative rule that ignored virtually every rulemaking requirement of the APA, it will be obliged to overlook that reality. Instead of simply terminating the program because it did not go through the requisite process, the agency will be compelled to treat an invalid legislative rule as though it were legitimate
President Trump’s Acting Secretary of Homeland Secu-rity inherited a program created by President Obama’s Secretary that was implemented without statutory authorityand without following the APA’s required procedures. Then-Attorney General Sessions correctly concluded thatthis ultra vires program should be rescinded. These cases could—and should—have ended with a determination that his legal conclusion was correct.
The key part here is that the majority held that the standards put forth in another decision simply called State Farm (where the government simply yanked a prior regulation) applies to the Trump administration's decision to rescind DACA as well. But Thomas' dissent notes that the original order was illegal, something the majority opinion never addresses. Even President Obama questioned its legality initially
Responding in October 2010 to demands that he implement immigration reforms unilaterally, Obama declared, "I am not king. I can't do these things just by myself." In March 2011, he said that with "respect to the notion that I can just suspend deportations through executive order, that's just not the case." In May 2011, he acknowledged that he couldn't "just bypass Congress and change the (immigration) law myself. ... That's not how a democracy works."
The risk here is that any order one President gives can then be held up in court if the court doesn't like its reasoning
I sincerely hope this case is a ticket good for one ride on the John Roberts express. This framework, if taken seriously–which I do not–would make it impossible for any agency to modify an old policy that is in effect. There will always be countless ways to address reliance interests. My prediction: the DACA case will soon be treated like the APA analysis in the Census case. Another blip in administrative law that was only needed for the moment.