Invalid read of size 8 – Valgrind + C

The problem is that you’re freeing the sym, then trying to access a value from the (now-freed) data: sym->next.

You probably want something like this for the inner loop:

struct symbol *next_sym = NULL;

for(sym = st[i]; sym != NULL; ) {
    next_sym = sym->next;
    free(sym);
    sym = next_sym;
}