This is all about priority. I'm a little hazy about the details, but from what I understand, once a chain has finished resolving, or a Normal Summon/Set has taken place, the turn player always has priority to activate another card effect (except Normal Spell Cards). That's why Exiled Force is so popular, because it can be Tributed immediately after it's Summoned for its effect, with no risk of having the opponent pull a Trap Hole on it or something.
The turn player always has priority (except when they declare an attack, I think). When the turn player chooses to end a Phase, they are passing their priority. The non-turn player (you) then gains priority to active a card or effect. That means you could indeed activate Threatening Roar out of nowhere, making it Chain Link 1 so it isn't actually activated in response to anything else.
When both the turn player and the non-turn player pass priority to start a new chain, then the Phase ends.
krishna said:
For instance if my opponent is looking through his hand and thinking about his options, I could just say "I activate threatoning Roar." even though it wasn't in response to anything?
I guess I was always under the impression that I did. ^^;
Probably just because that's how the video games operate...
So you can indeed just say "I activate Threatening Roar, or Call of the Haunted, or Survival Instinct, or whatever", without having to chain that card to something the turn player did.
However, the way you put it, while the turn player "is looking through his hand and thinking about his options", you CANNOT activate your Threatening Roar. That's because the turn player has priority. Only if the turn player says, "Well, I don't want to do anything else in this phase. How about you?" may you then proceed to activate Threatening Roar out of nowhere.
That's the only time (as far as I know) that the non-turn player can start doing things by themselves - at the end of a Phase. In the rest of the Phase, it's always the turn player who's doing something, and the non-turn player always responds to it.