Simply put, because the're not resistors but p-n junctions, and because of that their V-I ratio is exponential.
It doesn't mean that you can't calculate their current, just that it's not as simple as for resistors. For instance, you can treat them with a threshold model, with a fixed voltage drop. Then the current will be set by external resistors or active components.
The LEDs are diodes, so that's the obvious similarity. Also the base-emitter junction of a bipolar transistor is a diode, and behaves similarly. The only difference with diodes is that their threshold voltage is higher due to the different materials and doping.