This Letter reports a modeling study on the formation of streamer discharges from an isolated ionization column under subbreakdown condition. Numerical simulations show that positive streamers are able to form from the tip of an ionization column in a uniform applied electric field well below the breakdown threshold field. However, even when the applied field approaches the breakdown threshold field, negative streamers fail to originate from the other tip of the ionization column after the positive streamer has propagated a certain distance. The results reported explain some puzzling observations on streamer discharges in nature such as the predominant initiation of sprites by downward propagating positive streamers and help advance the initiation theories of sprites and lightning.