Why is paragliding not an old invention?
Paragliders as we know them depend on parawings with relatively high glide ratios and useful levels of steering.  Neither of these qualities were well represented in the round parachutes (even the so-called glide 'chutes) in common use before modern flat canopy glide parachutes came along (in the 1970s?).  Parawings as we know them were an outgrowth of these highly maneuverable parachutes, modified to have lower loading (for better sink rate) and optimized for horizontal flight, without the need to open in a near-vertical fall at terminal velocity.

If the knowledge had existed, parawings as we know them could have been built as early as the 1860s (when plain, round, uncontrollable silk parachutes came into use for stunt jumps from balloons).  The missing ingredient, as it were, was simply the knowledge that such a thing was useful and possible.