There's one very important aspect to read a person, and it's right in the description of the trigger: "When you read a person in a charged interaction..." If the interaction isn't charged, then the move doesn't trigger.
What is a "charged" interaction? At some level that's up to you as the MC to determine, but at the very least there should be some kind of tension going on. Someone is angry, hurt, exasperated, betrayed, lustful, passionate, etc. If two people are just shooting the shit over beers, that's not a charged interaction, it's just an interaction. No move is triggered. If two guys are having beers and one of them suddenly reaches down and unclips his holster for no apparent reason, well, the interaction has just gotten charged and maybe a move is appropriate.
So if your players are wanting to read a person all the time, ask them what they're doing to make the interaction charged. Make them establish in the fiction what's going on. At some level, read a person is about pushing people to see how they react to that pressure. So what are you doing to push them? Insulting them? Shouting at them? Or are you just giving them the stink-eye, or treating all of their statements as obviously suspect? Are you doing something that could be interpreted as threatening, either to them or someone they care about? Are you being obviously evasive? Or maybe grilling them in detail and demanding answers?
Or maybe they're doing that to you and you're trying to figure out why.
It is important for you and your players to establish what makes the interaction charged because it helps you know what happens next. This in turn is important because the other important thing to keep in mind is that rolls have consequences. Failing to read a person doesn't simply mean that you can't ask any of the questions, it is a miss, which means the MC can make as hard and direct a move as he or she likes. There is a good example in the book of flipping the player's move for a failed read a sitch roll, but the same thing can be done with read a person. Give the player a little discomfort by holding three and asking them what they intend to do, or how you could get them to leave this NPC alone, or whether or not they're telling the truth.
And most importantly, have the NPC act on the answers to those questions. So if the NPC knows the PC is lying, well, maybe that snowballs into another MC move, like announce future badness - "You and I had a deal, and I see now that you have no intention of keeping up your end of the bargain. Hey, boys, why don't you tell Mad Max here what happens in Bartertown when you bust a deal." Or if the NPC knows that the PC intends violence, he moves to arm himself. So maybe the MC's next normal move is to put someone in a spot. "So as you're talking to Hickey about the disappearances, he's looking pretty nervous. Eventually he leans forward and puts his hands on the table, and one of them is holding a gun. It must have been up his sleeve, because you never saw him draw it. He says, 'I think this conversation is over.' What do you do?" This establishes something in the fiction. It tells the player that if he wants to resort to violence as originally planned, it's sure as hell not going to come as a surprise, and the PC is risking harm in return.
And any MC hard move is open on a miss, including inflict harm. How could harm be inflicted or traded off a missed read a person roll you ask? Ever heard the phrase, "whaddyou lookin' at?" It's almost always a prelude to getting punched. Someone might have a hair-trigger temper and not appreciate you giving them the stink-eye. Or maybe you inadvertantly touch a nerve and the person reacts suddenly and violently; "You ask Marie about her son and next thing you know she's gone from zero to psycho in no seconds flat. She's on you and jamming a scalpel into you over and over and over like a goddamn sewing machine, screaming, 'You stay the fuck away from my son!!!'. Take three Harm and make the Harm move for me."
The thing to keep in mind is that read a sitch and read a person aren't generic perception rolls. You're never rolling to see if a PC spots some random detail. What you're rolling for is to see if they spot that detail when there's tension, when the consequences of spotting it (or not) are more important than the detail itself and bound up in the overall situation.