Ichorid
Creature - Horror 3/1, 3B (4)
Haste
At end of turn, sacrifice Ichorid.
At the beginning of your upkeep, if Ichorid is in your graveyard, you may remove a black creature card in your graveyard other than Ichorid from the game. If you do, return Ichorid to play.
Your opponent was right. The difference is between activated and triggered abilities. With activated abilites, you have to pay the cost upon activation. Ichorid, however, has a triggered ability. With triggered abilities, the "cost" has to be "paid" when the triggered ability 
resolves. Basically, when the triggered ability resolves, your opponent THEN gets to choose whether he'll sacrifice or not. So, just having the triggered ability trigger will not require him to sacrifice then and there. In fact, the triggered ability will trigger every turn and resolve every turn, even if he chooses not to remove a creature in his graveyard from the game.
410.5. Some triggered abilities’ effects are optional (they contain “may,” as in “At the beginning of your upkeep, you may draw a card”). These abilities go on the stack when they trigger, regardless of whether their controller intends to exercise the ability’s option or not. The choice is made when the ability resolves. Likewise, triggered abilities that have an effect “unless” something is true or a player chooses to do something will go on the stack normally; the “unless” part of the ability is dealt with when the ability resolves.