The reasons are the following:

a) From a technical point of view, SLRs and DSLRs work different than point-and-shoot cameras. The first thing, the light path hits after passing through the lens, is a 45 degree mirror which mirrors it upwards to the pentaprism (on the 10D) or the pentamirror (on the 300D) - and part of it is mirrored downwards towards the exposure and focus sensors.

Once you fully press the shutter button, the mirror is flipped up (you'll hear the mirror "slap" noise) and the shutter is openened in order to allow the light pass through to the sensor.

b) the way the CMOS sensor used in this camera works, doesn't allow for continuous image output, so even if there wasn't a mirror in the way, you wouldn't be able to get a continous stream of x images per second.

(nubui)