Zoo decks basically run a gambit that puts all their hopes and prayers into a few turns. It tries to isolate you to ~1/3rd of your deck vs ~1/2 of theirs.
I can't speak for everyone on deck design philosophy but my take on it is if you're worried about the match-up, start taking a random polling of 10 cards of your deck (and pay attention to sequence) and see how many are relevant to the match-up. One of the reasons that
Control Warrior is so great vs most the early game decks is it runs roughly 15-ish early game relevant cards (+a few outlier useful ones like Execute) that are good to see. You're looking at having something relevant in the first few turns around 80%+ of the time.
It's one thing to have plans for the early game (e.g., Watcher + Sunfury) but if you're running combo packages and they make up maybe 6-8 cards of your deck, you can't really count that as enough for the match-up. Not to say you NEED half of your deck to be anti-aggro but it's good to have a good number of cards that you're actively wanting early on so you can give yourself a well-above 50% chance to hit something good. It also works to give you obvious mulligan goals which helps a lot.
Plus, most of those anti-aggro cards are good generically. From a Shaman perspective, for instance, Feral Spirit is just always a good way to put pressure on the board. Having the spot removal stuff like Earth Shock, Lightning Bolt, and Lightning Storm tend to be nice to have as well. In Control Warrior, I'm fine with Armorsmith or Acolyte openers against basically any deck.
As Shaman, it seems like the only way I can beat Handlocks is with mass taunts - Feral Spirit, Argus, and Senjin Shieldamasta. Combo that with Hex, Earth Shock, and some burst from Leeroy/Rockbiter/Windfury and that's about my only hope to win.
Hm. Handlock (and Control Warrior) are the two decks that Shaman is basically best at. Earth Shock stops the Twilight Drake opener and Hex is enough for an early Mountain Giant. Flametongue, Windfury/Al'Akir and all the spells let you get them to 16-18 Health (or whatever their current Mana +3 is so they can't Molten + Sunfury unless you have a way to bypass one taunt) and burst them down in a single turn.