Essentially, I want to know if the copywriter can or should help us craft our 'why'.
Generally, a marketing consultant or strategist is the person who can help you define your brand, discover your unique selling proposition, understand your target audience(s), define your positioning, etc. The strategist can help you decide which story you want to tell, and why you should tell it. The strategist can work on the "whys" (why we were founded, why we do things this way, why you should hire us instead of the other guy, etc.)
The copywriter can take that story, and those "why" statements, and wordsmith them in a way that supports your brand identity and marketing strategy.
It's not unheard of to find both a crafty marketing strategist and a compelling copywriter inside the same body, but it's relatively rare. You will likely pay more for this breadth of service than you would for just a copywriter.