The following is an excerpt from CLRS:
The definition of $g(n)$ requires that every member $f(n) \in \Theta(g(n))$ be asymptotically nonnegative, that is, that $f(n)$ be nonnegative whenever n is sufficiently large. (An asymptotically positive function is one that is positive for all sufficiently large $n$). Consequently, the function $g(n)$ itself must be asymptotically nonnegative, or else the set $g(n)$ is empty.
Intuition suggests that having one function with a positive domain while the other with a negative one perverts the purpose of asymptotic analysis (a measure of the order of growth) as the positive function can be an upper asymptotic bound of the negative function simply on merit of it being positive, even in cases where the negative function grows faster.
In cases where both functions have negative domains, asymptotic analysis would still be a valid measure of the order of growth, making the restriction of both functions having to be positive appear useless.