I'm trying to remove the front sight from a typical mil barrel. I know that the pins are tapered maybe .003 or .004   I figured that they come out to the right, looking out towards the target.  I tried the usual machinist punch and hammer.  No dice. So I tried in the hydraulic press but without a jig to hold everything, that didn't work. So I tried the handy-dandy bench vise (6 inch). I used a parallel machinist clamp set to just wider than the pin to support the sight and the other vise jaw to drive the pin.  Once I got the setup in the vise and tightened it so I didn't have to hold on to anything, I tightened the vise as hard as I could.  The pin would not move.
What am I doing wrong ?  I'm NOT going to hammer on it for a nnumber of reasons.

Roger

Apply some penetrating oil and let it sit overnight.  Then try your vise method again; they really should pop out using that method.

If all else fails try applying some heat to the front sight base (goes without saying to be careful applying heat if you've already put oil on it).

I punched mine out with my 4" vise and no penetrant. Make sure you're pushing on the small ends of the pins, and that you only push on one pin at a time.

My method was to drill a dimple in one of the vise jaws, right in the center above the screw, to allow room for the large end of the pin while the other jaw pushed on the small end; I padded the pin's-large-end side of the front sight base with a piece of leather. Putting the assembly in the center of the vise, directly above the screw, works better than using the edges of the jaws because some vises will cant to the side if uneven pressure is applied, which prevents it from being tightened more. Just some bits of info.