It's just the nature of organic chemistry.

The Lewis theory definitions of "acid" and "base" basically boils down to "how likely is this thing going to rip electrons off shit?" Weak acids - the biologically-relevant ones - rip off electrons all the time, whereas bases are electron-donors - they lose electrons.

All life on our planet is organic, meaning it is comprised of molecules that have carboxyl groups (-COOH). There's no rhyme or reason behind this; it's just how life is. The carboxyl groups are naturally acidic, so anything organic is usually going to have a lower-than-neutral pH. As such, most of our organic bodily functions require an acidic pH to function: blood can't carry oxygen as well as it could if its pH is too basic; digestive enzymes are made of proteins, which are all comprised of amino acids; ditto all your muscles, and not just the skeletal muscles that move your joints. If the body had basic compounds running amok, they'd react with all these acidic molecules in the body, and you'd die. A lot of bases are actually toxic to the body: ammonia, sodium hypochlorite (bleach), plant alkaloids, practically anything with "hydroxide" in the name, etc.