The reason it's not an attack is because you cannot hurt your opponents deck with it. If you trash a card, it goes back to their deck at the end of the turn. Also, you can just as easily hit a hand with only victory cards, which is actually beneficial to the opponent.
There are a good number of exceptions: Ambassador, Masquerade, Spoils, Madman, Island, Outpost (Outpost would not hurt their deck, but would hurt their next turn), to a lesser extent Native Village, coin tokens. Also, you can use their deck inspection cards (like Apothecary, Navigator, Cartographer, even Spy, Duchess, Oracle and Survivors) as deck mockery attacks, and similarly with Mandarin, Inn, Scavenger, Count, Herbalist, Scheme, Stash and even Chancellor and Trusty Steed.
So, I am probably forgetting cases, but Possession can definitely be an Attack, in the sense that you can do things to their deck or turn you could not do in another way.
Also, lots of Attacks can benefit the attacked. You may want Curses to Ambassador or for Trade Rute or Forager fodder. Discard Attacks can activate Menagerie or Tunnel. Deck inspection Attacks may leave some dead card on top for you to Native Village away, and probably a lot of other cases.