In order to call a film a classic, it must meet several criteria, although opinions certainly differ as to when a film should or may be called a classic.
For me it is a classic if it has had a lasting impact on, changed or influenced the film world.
and Predator simply doesn't have that. It's a cult film, no question, but it's only that among fans.
Seen globally, it is "just" a very good action thriller, nothing more and nothing less.
But it didn't have a huge influence on the film world as a whole.
Frankenstein, Dracula, Jaws, Star Wars, 2001, The Godfather and also the first Alien. These are style-defining classics because after their release major changes and a jolt went through the film world and these films have left a huge influence to this day.
I love the first Predator but for me it doesn't meet enough criteria to be called a real film classic.