Do I have to give Facebook access to my phone's phone book to use the app?
Depends on what you mean by "Facebook" and "access". You have to give "WhatsApp" access to your photos and contacts list and device storage. There is no agreement that they own or can look at any part of what's stored in those places - it's just mechanical access to the folders these things are stored in, not free access to use or take the contents for their own purposes. The reason they need access is not to operate independently, or scan your photos to glean information from them. It is so that if you decide to send a photo to a person on your contacts list, the app is allowed to open your gallery and your contact list and make that connection.
And FWIW, I don't use any messaging app at present. Email and texting is good enough "messaging" for me.
WhatsApp needs the same access for the same reason as your built-in text messaging app. If your phone didn't come with a default one built in, and you tried to install the app you are currently using, it would popup to prompt you for pretty much the exact same access - it's mechanical access to the folders, so that you can then use the contents of those folders yourself.
One thing I absolutely hate about Facebook is the way they sell your personal information, or use it to push ads at you, or use it for more nefarious ends. I'm disinclined to get the app just because I don't want Facebook to make money off of my use of it.
For the Facebook app in particular, there is a user agreement that lets them use your personal information for their own nefarious advertising purposes (I accept this for myself and consider it to be the fee they charge for me to use the otherwise free app). This is UNRELATED to the popup window asking you to give the app access to your photos/contacts/storage/etc.
As far as I know, this is not part of WhatsApp. To date, there has been no advertising in my use of WhatsApp. Maybe within the voice/video portions I don't use there are ads or something? I don't actually understand the business model of WhatsApp - I know that by using a free app, I am the product. I just haven't yet fathomed how I'm being sold.