Speed. You'll always stall if you go too slow to get enough lift. Putting the flaps down increases lift and drag and lowers the stall speed.
As for why the article mentions decreased lift whereas flaps down increases lift, that's maybe a bit more complicated. Lift vs. Angle Of Attack is a curve that tops out at about 15°.[0] Flaps often go to steeper angles than that, but I'm not sure if lift actually starts to decrease again in that scenario. Certainly adding a curve to the back of the wing (flaps) isn't quite the same as changing the angle of the entire wing.
> You'll always stall if you go too slow to get enough lift.
The amount of lift needed is determined by the load factor. In a turn, or when a glider launches via a winch, the load factor is higher than in level flight.
This means that the stall speed varies with load factor.
On the other side, you can still not be stalled below the straight and level stall speed, if the load factor is low enough. In parabolic flight you can see this, and with a load factor of 0 you cannot stall.
As for why the article mentions decreased lift whereas flaps down increases lift, that's maybe a bit more complicated. Lift vs. Angle Of Attack is a curve that tops out at about 15°.[0] Flaps often go to steeper angles than that, but I'm not sure if lift actually starts to decrease again in that scenario. Certainly adding a curve to the back of the wing (flaps) isn't quite the same as changing the angle of the entire wing.
[0] https://commons.wikimedia.org/wiki/File:Lift_curve.svg