If you've ever seen a maypole dance that's exactly how the braiding is done over this hoses. VERY different process and machines though.
You can weave in circles though and that is how things like fire hoses are made.
With weaving you have warp and weft yarn that are moving mostly or truly orthogonal to each other, like your jeans. One direction of yarn interlocks with the other, there is no interaction between yarn moving in like direction. An exception to this is leno weaving used for carpet backing and other things where two yarns will cross back and forth to lock with each other.
In braiding, you only have yarn in one direction and there is interaction between all of those yarns as they go back and forth. Shoe laces, hair, cover of paracord *same exact process as making these hoses btw*, most ropes, cave line, etc are all braided.