We might be able to start by trying to fathom why a flag flutters in a breeze. If one considers a soft (non-battened) airfoil they may do well to consider the material it is made of. Many sail fabrics stretch and contract with wind drag, resulting in a disruption of the airflow that holds the soft sail shape. Woven titanium may have less of a tendency to do this (wind tunnel study).
Sails, the obvious application, are not designed at all to function at low angles of attack as sail boats can only point so far into the wind before they lose forward propulsion. The "luff" or flutter is a good sign to increase the angle to the wind and allow it to "fill" the sail.
This might lead one to believe bottom pressure holds the sail shape, and indeed, at higher angles of attack, the suction peak moves forward, helping propel the boat. At lower angles of attack (with a soft thin undercambered airfoil), inconsistencies and turbulence under the wing will cause changes in its shape, which affects the airflow above. Local pressure fluctuations then cause the "luff". Battens$^1$ help prevent this.
One may imagine sails at higher angles of attack to be "stalled", but we must remember they are not required to produce "lift" (which would force the boat sideways), only thrust from the forward suction peak.
Aircraft airfoils simply are different in that they must support the aircraft weight with as little drag as possible, and any "luffing" would be disastrous. Therefor aircraft airfoils must be supported to avoid sudden collapse at low or negative AOA.
Although non supported airfoils may be possible for ultralight aircraft, they would carry higher risks best avoided, particularly with two separate wings as compared with a parachute, delta, or Rogallo wing.
$^1$ see performance of cambered battened sails