Maybe one would need to think about entirely different sewing patterns (that must look the part) and cloth stretching/folding mechanisms for this problem.
It's easy to see why you (with current technology) can't simply "make a robot that does what the human does" here.
Take something like the humble T-shirt. The process of making those is way more "automated" than it was even 30 years ago. The reason for this is that the t-shirt hasn't changed THAT much in 30 years, and is now more popular than ever. Due to the material, and the pattern, there is a lot of it that is the exact same step between product variations (size, cut etc) or can be done on the same machine the same way.
However, something as simple as pants, not only change seasonaly (shorts) but they change annualy. It is easier for a car manufacturer to build an automated assembly line for welding a frame, than it is for a manufacturer of clothing to do the same for "this seasons" hot item.
For the sake of argument, if we all agreed to wear bellbottoms for the rest of time as our only pants, and to only make them out of one kind of denim, it would STILL be hard for all the reasons mentioned above, but we would have reason to automate (scale). Even then, your producing the pants in 60 some odd waist/lenght combos for men, never mind women, children, teens.
So, the technology exists, more or less. Like all new technology, it takes time to roll out.
It turns out it's ridiculously difficult to make machines that will reliably deal with small, flexible, sometimes-overlapping, sometimes-folded, identically coloured bits of fabric.
You can automate parts of the garment-making process - embroidery, cutting things from rolls, stuff like that - but sewing the bits together automatically is really difficult for a machine, compared to a human.
If you've got clever solutions for this feel free to advance the technology - I'd really like a robot that can do my laundry :)