The Cayman islands are a well-known tax haven. Sorry to say.
Economists, in journals, routinely refer to the Cayman islands as a tax haven. Just a few examples out of many thousands:
https://www.nber.org/system/files/chapters/c14730/c14730.pdf
https://eprints.lse.ac.uk/56125/1/__lse.ac.uk_storage_LIBRAR...
If you want to know more this is a thorough review of the Cayman islands and their role as a tax haven: https://www.tandfonline.com/doi/pdf/10.1080/09692290.2016.12...
The main reason for having a subsidiary in the Cayman islands is to avoid paying taxes. In some cases this is legal tax avoidance, in others it is illegal. The ratio of the two is unclear because of secrecy laws.
One common way businesses legally avoid taxes (note that legal is not moral, many people think should be illegal) is through IP. They make money in country X, then their subsidiary in the Cayman islands has to be paid because it owns the patents involved, but that subsidiary is owned by the main company and sends that money back with zero taxes. In country X the profits look very small now because so much had to be paid in licensing fees.
Another way is through round-tripping money. Investing in the Cayman islands and then taking that money and investing it back into their country as a foreign investment.
There are countless other ways. The Cayman islands along with a few other tax havens play a nasty and selfish role in today's financial system that gives rich companies and rich people a massive advantage while hurting everyone else, while of course generously skimming something off the top for themselves.