Applying the Master Theorem on Merge sort
You can't use $n/2$ since this bound just isn't always true. Suppose that $n = 5$. It is not the case that you can split an array of length 5 into two arrays of length 2.5. It's not even true that you can split it into two arrays of length at most 2.5. But you are able to split it into two arrays of length at most $\lceil 2.5 \rceil = 3$.

Note that the textbook estimates the time it takes to sort an array with at most $n$ elements (rather than the time it takes to sort an array with exactly $n$ elements).