This is claimed by Jared Kaplan in his Lectures on AdS/CFT from the Bottom Up.
It seems that all QFTs can be viewed as points along an Renormalization Flow (or RG flow, this is the name we give to the zooming process) from a ‘UV’ CFT to another ‘IR’ CFT. Renormalization flows occur when we deform the UV CFT, breaking its conformal symmetry. [...] Well-defined QFTs can be viewed as either CFTs or as RG flows between CFTs. We can remove the UV cutoff from a QFT (send it to infinite energy or zero length) if it can be interpreted as an RG flow from the vicinity of a CFT fixed point. So studying the space of CFTs basically amounts to studying the space of all well-defined QFTs.
Why is this true?
Especially, how can we see that we can only remove the cutoff (i.e. renormalize) if the QFT "can be interpreted as an RG flow from the vicinity of a CFT fixed point"?