You don't seem to understand the ramifications of game language, or you are presenting the options poorly.
I think based on your post we run different playstyles at the table.
To a player, this reads as "the orc chieftain has succeeded in persuading you, as your resistance has failed. Having failed, your first option is to capitulate to the chieftain. Your second option is to hesitate. Your third option is to try to convince the GM of any other action, but the GM gets to say that is not an appropriate action. Pick one."
You as player get to decide.
1 and 2 would be options I came up with to help the players. idea-wise.
3 would be the player gets to be creative, with the limitation that your action has to make sense in the fiction for the table.
My experience has show it is not that hard amongst friends.
Few if any players are going to interpret that as "I am allowed to debate the situation and make my own decision, including not trusting the orc and attacking."
Lowering your shield, taking a step back and looking at your companions it not the end of a scene.
Why you saw it that way is on you.
I'm not running the entire social encounter here, I'm reflecting the use of Persuasion by an NPC in a way that is not overly powerful as some may fear, and also not so binary/boring. It is merely an example of how you can approach skill-use by NPCs.
Furhermore, the "option" of failing the check intentionally being offered as a defense of interesting roleplay is quite the strange offer, when it reads as "...and the GM gets to say what you do.".
I find the misreading of it strange.
Players can select that their characters are persuaded. Full-stop.
Players who who wish their characters not to be persuaded set themselves a DC.
If the Chieftain succeeds then they select 1-3 as an immediate response.
The social encounter can continue, but I expect the stakes for Persuasion will increase or it may change to Negotiation or combat may break out, but the latter MAY create/set a strong basis that may be used (by the table) against or for that character's actions in the future.