Older chains (5,6-speed era) used thicker sideplates and longer pins and would tolerate having the pins pushed out and back in to remove and replace the chain.

Newer (8-speed and above) chains are much narrower, have thinner sideplates and the pins are flush with the sideplates. To make these pins strong enough, the ends are flared or riveted in place. So, pushing out one of these pins wipes off the flair and reams the sideplate hole a bit oversize and pushing it back in leaves a much weakened connection. Do not do this.

Shimano and Campy have specific joining pins that must be used to replace a standard pin if you push one out. KMC, Wippermann and SRAM offer reusable master links to join their chains. These links are also sold as aftermarket parts and the KMC or Wippermann links can be used on Shimano chains in place of the joining pin. Obviously the replacement pins or master links must match the chain width which is specified by the number of "speeds" (cassette cogs) it's designed for.