Why doesn't subset sum solution violate Exponential Time Hypothesis?
Given a 3SAT problem of size $n$, you can convert that to a subset sum problem of size $n^2$ (roughly).  Now you can apply the algorithm for subset sum to solve the subset sum in time $2^{n^2/2}$ (roughly).  Remember, the running time depends on the size (length) of the input, and here the size of the input will be $n^2$, yielding the $2^{n^2/2}$ figure.

That will give you an algorithm for solving a 3SAT problem of size $n$ in $2^{n^2/2}$ time (roughly).  But that's much worse than the naive algorithm, which takes $2^n$ time: $2^n$ is much smaller than $2^{n^2/2}$.  So this reduction does not contradict the exponential time hypothesis: it doesn't give you a way to solve 3SAT faster than $2^n$ time.