It is a joint venture. US taxpayers want to support Israel's right to exist, and especially for a defensive anti-missile system that works. The US may need to use it to defend against missile attacks on us or other allies. There is a real and present danger that allows the system to be tested, improved, and retested.
The right question for you to ask is why are other nations not paying for this?
Why isn’t Israel paying for it? We should be spending money to defend our borders, not theirs.