The answer to 'why is my sink rusty water' is that the rust is likely coming from the plumbing pipes or fittings underneath the sink. Rust can build up over time in metal pipes, especially if the water has a high mineral content or the pipes are old. This can cause the water to take on a reddish-brown color as it comes out of the faucet.
Some common causes of rusty sink water include corroded galvanized steel pipes, worn-out brass or copper fittings, and mineral buildup in the plumbing system. If the problem is isolated to just the sink, it may be possible to fix it with some basic DIY plumbing work. However, if the rust is coming from the main water supply lines, it's best to call a professional plumber to diagnose and repair the issue.