Why doesn't a "Both" option exist for situations when both statements describe me well, or when neither statement describes me well?

The omission of a Both option was intentional.

The research that led to the Clifton StrengthsFinder revealed that people are not "well-rounded" and that your best opportunity for strength lies in your greatest talents.

Rather than allow you to say you are good at everything, the assessment helps you sort and rank your talents as your instincts guide you -- just as you naturally do throughout each day.