Because you try to store possible future moves.
Therefore you need to store all possible moves for the future.
Assuming you have 32 chess pieces and every piece has 4 possible moves it can do you would need to store :
1 Moves: 128 Possibilities
2 Moves: 16384 Possibilities
3 Moves: 2097152 Possibilities
4 Moves: 268435456 Possibilities
5 Moves: 34359738368 Possibilities
6 Moves: 4398046511104 Possibilities
7 Moves: 562949953421312 Possibilities
8 Moves: 72057594037927936 Possibilities
9 Moves: 9223372036854775808 Possibilities
Thats just a simple assumption of the number of pieces and possible moves, but you see that even for 3 moves ahead you need to save around 2 Million possibilities, which is a lot if you have limited time for each turn.
For sure you could make optimizations and stuff but to answer your question:
Because you neither have the CPU-speed, nor the HDD-space to save a whole list
of possible moves.