Yes, many Western countries are frightened of the emergence of China. The reason for their concern has to do with economics.
Fundamentally, the rise of China represents a existential threat to Western Economic Hegemony. The Western world, being the first to modernize, reaped a first mover advantage economically. Below are the mechanisms of Western first mover advantage:
Brain Drain - the smartest, most ambitious people in the less developed countries desire to move to Western countries for better economic opportunity. This gives the West a greater supply of talent than what they produce domestically
Corporate Power - The C-level positions in many large companies are disproportionately held by whites. This is the case even when Asians make up a large part of the company’s high end work force.
Reserve Currency - for the longest time, the currencies of the Western countries were viewed as safe and stable. This cause capital flows to Western government bonds which lower their interest rate giving Western governments more flexibility to deficit spend
Capital Flight - the questionable governance and corruption of less developed countries cause their elites to offshore their wealth (either rightfully earned or stolen) to Western bank accounts and assets. This drains the developing countries of investment capital while enriching the Western countries.
So let’s analyze how China’s emergence threatens all the above advantages for the Western countries:
I’m going to bundle 1 and 2 together. When China becomes economically strong and also invests in their neighboring countries through their Belt and Road initiative, this will create more economic opportunities in the developing countries and reduces the desire of their most capable people to leave for the West. They will be able to get jobs and start business near their extended families instead of relocating.
On the corporate level, the Western companies will receive fewer qualified Asians. On top of this, the qualified Asian workers of theirs might even leave for home and form competing companies (see NReal as an example). So it becomes a double loss, first fewer capable workers and new fearsome competitors created by their former dissatisfied workers which erodes their pricing power.
A similar thing will happen on the financial level. Money from the Asian and Belt Road countries will no longer flow as much to the West. With better opportunity and governance, their money will be reinvested in their own countries instead of real estate in London or LA (as an example). Better governance also means less corruption and thus fewer corrupt officials looking to launder their ill gotten gains through Western financial institutions.
On the government level, this couldn’t happen at a worse time. A huge cohort of (white) westerners are aging their way toward retirement and the payouts promised by government welfare programs such as Social Security and Medicare. These programs are basically being funded by debt since the payroll taxes do not generate enough income to pay full benefits. At the state level the governments have racked up massive unfunded liabilities in the trillions of dollars.
If China is able to reduce capital flows towards the West, then these programs will become unaffordable and collapse right at the worst moment.
Imagine the social unrest this will create. This will make the BLM protests/riots look like the appetizer before the main course in comparison.
The Western world have been complacent and have been living above their means for quite some time. China will be the mechanism which expose the Emperor for not wearing any clothes.
hope it helps.