Well, England had a massive trade deficit, and failed to find anything the Chinese wanted to buy, except opium. In the end, this was approved by the queen to balance their trade deficit, as they were bleeding silver.
How is it possible that the England had nothing China wanted to buy when England was so technologically superior that they were able to defeat China's military, fighting in China, on the other side of the planet, outnumbered 10 to 1?
The same smugness and sense of superiority that China held for England, was also held by England for China. As such, the English only primarily tried to sell knickknacks and things the Chinese could produce better. This ended up backfiring and cementing the view to the Chinese that the English were simple barbarians.
They did indeed have weapons the Chinese (and other nations) wanted, but only sold a limited amount of them, to avoid arming the other nations too well, in case they ever wanted to go conquering.
You're correct that British made factory goods would have been good for China, specifically the Chinese poor, as it would have enabled them to have many low quality goods rather than a few higher quality goods.
The issue is that when you present goods like mass produced clay teapots, cotton textiles, etc to the customs agents of the country which invented fine china, and silk, you're not going to impress them.
And yes, Britain coveted China. As did Japan, Russia, Germany, The United States, France, Italy, and Austria-Hungary. Even after they won the opium wars and got their favorable trades, they continued to work to overthrow or minimize the Qing dynasty and take political power. The Qing ended up sputtering out a few years before it became unfashionable to be a colonialist, so China dissolved into rule by warlords, then conquered by Japan, then the communists won and the rest is history.