This is too long - sorry. My 3 year old pinches. A lot. Myself, dh, dd, pretty much everyone who is close to him (he doesn't seem to do it to other children oddly).
This has been going on since he was a small baby in a way. It started with him pinching/rolling/grabbing my breasts when he was nursing. I tried really hard to keep his hands at bay & would even limit his nursing if he was being too rough or too insistent with it. I tried to replace my breasts with other objects for him to play with but he had no interest.
For the past 1.5 years it has been what he is doing now. He'll hug you & give you a little pinch on the back of the arm. He'll randomly come over & pinch a cheek or your leg. He'll be playwrestling with dh (something he does with very strict rules about what is ok & is not ok) & pinch. He particularly likes the soft, saggy skin of my mil's arm or neck.
I've watched reallllllly closely to see what triggers it but there is not cut & dry obvious thing. At times it is most definitely an uncontrollable urge for him - we've even seen him trying to control the urge with his fingers poised to pinch & shaking. These times actually don't bother us so much 'cause it is obvious there is something else going on here (of course we would love to see it end).
It's the deliberate times. Sometimes it is to get attention - especially when he does it to dd (3 mos) but other times it's not even for attention, it's almost more out of excitement.
This has been going on for a long time & at NO time did we not deal with it. When he was really little we would simply hold his hand & figured he'd outgrow it. As he got bigger we would physically remove him from us (and I'm not kidding when I say this could mean removing him from us hundreds of times in a day sometimes).
As he's gotten older I've yelled (not my favourite thing but everyone has a limit), we've discussed it calmly, we've given him options of other things he could pinch (a teddy bear, etc.), given timeouts (VERY time consuming for our day) & most recently I will admit I have pinched him back out of pure frustration & because he refuses to accept when we tell him it hurts (he is very insistent, to the point of tears, that it tickles).
I do NOT want to hurt him but we cannot keep up with this. He is 3 & I feel he is old enough to at least be making an attempt to control himself but the deliberate attempts seem to be ramping up. I am finding myself becoming increasingly short & irritated with this action.
We have tried very hard to be consistent with whatever tact we were using (with this going on for so long we've had plenty of time to try different things for several weeks at a go for each) & include our parents in what we are doing.