It depends on the type of social conflict.
If Empathy is to be used in a social conflict as an "against": it's usually that Deceit would be rolled against empathy. You are attempting there, to use your empathy reading to tell if someone is deceiving you or not. In turn, a PC trying to lie would be their deceit vs the other character's empathy roll.
But for what you are specifically saying: How I run as GM, usually (there are exceptions depending on the conflict), is that you would rolling against Will, to convince someone to do something. As it is trying to convince them against their conviction not to.
Rapport (ability to talk someone into) vs Will (ability to hold your decision/will to not spill the information).
To back up this assertion, the fate website (fate-srd) lists a "will stunt", specifically for social sort of situations:
Indomitable: +2 to defend against Provoke attacks specifically related to intimidation and fear.
Speaking of: Provoke is also essentially intimidation, it doesn't have to be physical harm. It's a social skill/riling someone up through that:
Provoke is the skill about getting someone’s dander up and eliciting negative emotional response from them—fear, anger, shame, etc. It’s the “being a jerk” skill.
And so, provoke could still work: it would still be pitted against will. It's just a matter of what kind of approach to convince is being used.
"You better tell me you coward" (provoke) / "Listen, here's why you should tell me" (rapport).
Here is more on what the website has to say, as an example of a provoke vs will social situation:
Okay, Fine!: You can use Provoke in place of Empathy to learn a target’s aspects, by bullying them until they reveal one to you. The target defends against this with Will. (If the GM thinks the aspect is particularly vulnerable to your hostile approach, you get a +2 bonus.)