You are in danger of making the Lump Of Labor Fallacy:

http://en.wikipedia.org/wiki/Lump_of_labour_fallacy

You are looking backwards. That is your first mistake. If you only look at what jobs exist now, then you are forced to look backwards and everything looks dark. Try to imagine what the future might actually be like.

Let's take a hypothetical example of some future industry:

It is well know that by the year 2050, the urrgh industry was central to the USA economy. Conceptually, the idea of urrghs was developed by Lisa Simon Beckworth of MIT, late in 2014. Michael Ardossa of Stanford developed the first working urrgh in the summer of 2016. However, urrghs remained an academic toy until 2019, when Herbert Boink of Cambridge developed a technique for mass production. Early in the 2020s it seemed like a number of old names from the tech industry were also going to dominate the urrgh industry: Sony, Samsung, IBM, Lenovo. However, it soon became clear that the old tech companies had the wrong kind of management structures for pioneering the new industry. A host of newer companies sprang up. The public only gradually became aware of urgghs. Many people point to 2026 as a turning point. If you measure the number of articles being written about urrghs in the popular press, there is a 10x jump between 2025 and 2027. By 2028 there were young people confidently describing themselves as "urrgh professionals", the implication being that they were going to make their whole careers in the new industry. The early 2030s saw explosive growth in the industry. After the recession of 2038, economists pointed out that the urrgh industry had been the leading cause of economic growth during the last business cycle, and would likely play a major role in the next business cycle. On the eve of the next recession, in 2046, the urrgh industry was employing 1 million people in the USA.

We all know at some point in the future there will be some new industry that sweeps the world and generates a lot of economic growth. The only question is how much any one given nation will dominate that industry. But that raises a different issue, an issue about national competitiveness, which should not be confused with issues of one nations unemployment, unless you want to make the explicit argument that some nation is stealing jobs from some other nation. Which can be true in some circumstances, but those circumstances need to be made explicit, for the conversation to have any meaning.

The thing is, it's hard to know what the next big thing is. Generally, those countries that have the fastest growth in productivity also have the lowest unemployment rates. That might seem counter-intuitive, until you think about what productivity allows: it means you can produce more, at the same or higher quality, than you did before. If your productivity goes up at 10% a year, and your competitor only goes up at 5% a year, then pretty soon you can make more of whatever you make, at higher quality and lower cost, than your competitor. This applies to nations as well as companies. Back when Japan had 7% productivity gains every year, and the USA had 2% productivity gains every year, Japan had close to 0% unemployment. But if you believe, as you suggest, that rapidly rising productivity increases unemployment, rather than reducing it, then you would assume that Japan would have higher unemployment than the USA, back when its productivity was higher. But we know the opposite was true.

Even worse, if you took your own argument seriously, then you would have to argue that falling productivity is a good thing since it would mean more jobs for everyone. But I assume you are smart enough to avoid doing that.