If you get an individual fibre bundle and handle it, the individual fibres that make up the fibres can fluff up relative to each other.
This means they either need to be set in resin or they need to be protected in other ways. Set in resin it is not really very clever with abrasion however we often need to protect carbon from abrasion and do successfully with other materials.
Whilst it is true that carbon suffers when it is forced to take high loads in tight radii.
The thing is your waist, even if you are a child, isn't a tight radius in engineering terms.
As an example I have taken the entire primary rig loadings of a 40′multihull yacht through carbon bent to a radii of 2″ successfully.
Even if you look at the fibre deflection in weaves to make commercially available fabric the tow clearly takes a radius.