IMO pushing is a technique of desperation.
You give up detail at the bottom end, in exchange for faster shutter speed.
The extra development moves the left-overs up higher on the curve into a more usable range. This effect is greatest in the highlights and least effective in the shadows.
The ISO standard has a safety factor so some underexposure is doable without loss on the print, the negative though still loses detail. Underexpose enough and it effects the print.