Why isn't the universe uniform and symmetric?
Entropy of the universe keeps on increasing.
Our universe follows the second law of thermodynamics, which states that the total entropy of an isolated system always increases over time, or remains constant in ideal cases where the system is in a steady state or undergoing a reversible process.
'Uniform' and 'Symmetry' are terms which are related inversely to entropy (They are basically the opposite of what entropy actually means). And so, our universe is not uniform and symmetric.
As it is mentioned in Wikipedia:
"The increase in entropy accounts for the irreversibility of natural processes, and the asymmetry between future and past."
Hope this helps!