Why do people consider DACA unconstitutional?

Why do people consider DACA unconstitutional?
I’m looking for an answer more specific than “the Obama administration exceeded its authority.” I know that’s the ultimate reason it would be unconstitutional, but I don’t understand how to get to that conclusion… I also know that many arguments for or against DACA’s constitutionality fall along partisan lines, which doesn’t help me clear up my confusion.

I have never studied law, so although I do my best to try to understand it, I know I make mistakes.

But anyway, here’s where I’m coming from:

DACA grants deferred action (to be renewed every 2 years) and work authorization to undocumented immigrants that meet certain requirements. That’s it, right?

From what I understand, well before DACA, the DHS already had the ability to grant undocumented immigrants a deferred action status (part of their “prosecutorial discretion” for immigration cases), and they also had the ability to grant work authorization to immigrants with deferred action status. (This recent letter goes into a bit more historic/legal detail). These powers were both established decades before DACA was a thing, and were used by previous presidential administrations.

The only thing that seems different with DACA, from what I can see, is that the Obama administration laid out explicit parameters it would look for when granting deferred action—telling people ahead of time whether they would qualify. Why would that be unconstitutional? Why would it be considered legislating from the executive branch? I feel like I must be missing something here.

I know that Texas (and 25 other states) sued over DAPA and DACA+, and while the case was never officially ruled one way or another, the injunction held. They argued the Obama administration had violated the Administration Procedure Act of 1975 by failing to perform certain procedures prior to implementing DACA. I don’t really understand the act, beyond a vague concept that it defines the procedures administrations must go through when implementing new rules?… (Or implementing new rules that overlap the duties of other branches of government?)… My question here is: Why does APA apply to DACA? What makes DACA a new rule, rather than new packaging of old rules?

Where does my understanding of DACA differ from those who view it as unconstitutional?