Why can't echoes be heard inside a room?
You just haven't tried a big enough room...try a large, empty gymnasium or something similar (but not a concert hall as they are usually designed to suppress echos.).
The speed of sound is roughly $v_s = 340\text{ m/s}$ (1100 feet per second), and hearing an echo requires at least
- a perceptible time between the end of your shouting and the onset of the returning wave (not sure how long, but lets say $t_c = 0.1\text{ s}$ as a guess (a lot of human perception works on time scales not to far from that))
- that the returning wave be sufficiently loud to be distinguished above the background noise
- that the returning wave be sufficiently distinct from the returning waves from other surfaces
- a surface that gives a good reflection
So lets think about how a indoor situation might fail:
The room is too small. If the longest dimension is much less than $v_s*t_c \approx 34\text{ m}$ then the maximum delay between the end of a loud shout and the onset of the echo may be too short for you to distinguish the echo
The multiple returns from the several walls are overlapping and preventing you from picking out one echo.
The ventilation system and other ambient noises are comparable in volume to the echo.
The walls may be non-flat or made of materials that absorb much of the sound energy (this is often a design goal for large spaces)
Sound does echo inside a room but you might not notice it much for two reasons.
Firstly the time for the echo to return is very small so you will not hear a long sound repeated as an echo, instead you will get a resonance type echo, like when you sing in the bathroom.
Secondly most rooms are full of soft furnishings that quickly absorb the sound and damp the resonance.
If you are in a large room with no furnishings and you clap once loudly you will certainly hear the echo rebounding rapidly off the walls.