No it's not, a major technological advancement was a machine that sews for you, there is very little hand sewing done any more. The second perhaps more important technological tour de force were the weaving machines, there is even less hand weaving than there is hand sewing.
The problem with the term "hand-made" is how vague it is, you would not a call a car "hand made" even though most of the parts are put together by hand.
Personally I think the sewing machine was a trickier problem than the weaving machine, We take them for granted today but it took 100 years and a real stroke of genius to figure out how to invert the process in order to make it simple enough for a machine to do it. while weaving has always utilized complex machines to make it possible.
Like your parent, I would consider that cars are, in the same sense, "hand made" both including the small runs of luxury cars (which are "hand made" in the sense where parts might not fit properly because the panel was made by Steve on Monday morning, and he got the measurements a bit wrong) and a generic mid-range SUV that Ford churned out in huge numbers where a "production line" still has humans working on every vehicle, even though they have machines to help them do a consistent job.
We should distinguish two kinds of weaving machine, fortunately my sister is a textile artist so I have to hand exactly the best examples. A few minutes walk from her home is Saltaire, which today is a tourist attraction but was historically economically important. Titus Salt's mill, for which the village provides housing and so on, had the second kind of weaving machine. The Mill produced fabric much like you'd see today, yards and yards of identical material woven at incredible speed.
But for centuries before such mills were built, the first kind of weaving machine had existed. You won't see many in use today, some kinds of University might show them to students, a few museums have one that can be demonstrated. But on the Outer Hebrides there are lots, and that's because Harris Tweed is specifically required to be made this way, on those islands, the same way Champagne has to be made in a specific way in a particular region of France.
It is in principle possible for humans to literally weave fabrics by hand, but it's ridiculously laborious, so the first machine (the one used to make Harris Tweed) makes a lot of sense. But if we're going to (and ordinarily people do) insist this counts as Hand Weaving then it seems also reasonable to say that operating a sewing machine to make a pair of jeans is also hand making clothes.
https://en.wikipedia.org/wiki/Sewing_machine
https://en.wikipedia.org/wiki/Loom
The problem with the term "hand-made" is how vague it is, you would not a call a car "hand made" even though most of the parts are put together by hand.
https://www.youtube.com/watch?v=cTZ3rJHHSik (Model T Ford Assembly Line) https://www.youtube.com/watch?v=MQPFVouph-w (honda factory tour) here are two car assembly lines 100 years apart notice how many people are still required to do final assembly.
Personally I think the sewing machine was a trickier problem than the weaving machine, We take them for granted today but it took 100 years and a real stroke of genius to figure out how to invert the process in order to make it simple enough for a machine to do it. while weaving has always utilized complex machines to make it possible.