During my lactation studies, they basically have the philosophy "if you can gestate, you can lactate"! Around 95% of women can sucessfully breastfeed their babies. However the most common concern for new mums is lack of supply. For the most part,if you demand feed (baby led feeding) and do not have more than 4 hours between feeds you will make enough milk for baby to thrive. THis said, it is vital that the mother have an adequate diet, especially rich in essential omegas. If attachemnt is a problem, and you don't have to have sore nipples to have an attachment problem, supply WILL ALWAYS suffer. It is true, if you have been really stressed through labour/caesear you will have delayed lactogenesis II (milk coming in). During this time it is absoluelty critical to have as much skin to skin contact as possible and allow baby to stoke, nuzzle and feed.
I have met 1 mother who COULDN'T breastfeed, she had NO breasts,she'd had breast cancer and had them both removed.
But there are other condition that decrease milk production, such as an underlying medical reason, frequently one that is undiagnosed.

Personally, I had undiagnosed coeliac disease (gluten allergy). I found out when my first born was 10 months or there abouts. I knew I had a low supply, but was told otherwise by professionals who didn' t listen. They you got your do gooder types who told me it was ok to FF. I continue to breastfeed my son, now 3 AND my 6 month old girl. At first with my son I breastfed 20 hours a day, (while studying my midwifery degree) and expressed after each feed for about 9 months. WHen he went 2 hours during the night I'd wake up and express in between, I'd be lucky to get out 5 mls. I never felt a let down. I do with my girl though. I stopped expressing by the time he was about 18 months because he was having adequate solids to support his nutritional requirements. Hard work but worth it. I looked at it as short term hard work, long term gain. I helped feed my nephew for my SIL when she was having breastfeeding troubles... now that was a long night lol.

Other reasons: breast surgery, particularly reduction surgery when the nerves are cut.
lack of breast development, ie, look like male breast tissue.
Baby might have tongue tie which needs simple operation
cleft palate can make it difficult.

I'm sure there are other reasons, just cannot htink atm.. In reality though, there are very few common reasons. With good management and advice 95% of women CAN breastfeed. It is just getting access to this good advice that is hard.