Many of the new kitchen faucets are having issues.
As the cost of materials go up the manufacturers keep making the faucet parts smaller and cheaper. This causes them to break or clog up faster than ever before. The slightest of particles can clog them to where they will not allow water to pass through.
Most times the issue will be in the strainer at the end of the faucet, but the issue can also be in the mixing valve, (also known as the cartridge). If the water still won’t flow it will likely be a clog in the feed tubes.
For the avid DIY’er taking apart a kitchen faucet is a fairly simple task, except when they hide that little screw or clip that you need to take off.
Here is a great video with some tips on diagnosing and repairing these issues.