It's not so much that a DSLR is the only way to shoot with a shallow depth of field (which can even be achieved on a phone camera if you're taking a picture of a ladybug a few inches from the lens), but that the greater the aperture and/or sensor size, the further away you can get a shallow depth of field. So on an APS-C sensor with an f/1.8 lens, you can shoot a portrait with the same level of bokeh you might only get with an extreme macro on a pocket camera, and on a full-frame sensor with an f/1.2 lens, your subject might be standing many feet away and you could still achieve the same effect.