Well, because Congress passed the Federal Arbitration Act, which says it's legal.
Depending on your views, you might also note that American courts are ruinously expensive and many people are denied access to justice because they can't afford to go through the legal process - which a cheaper parallel system can help with.
Or with different political views, you might note that because the powerful elite get to write the contract, the powerful are only subject to arbitration when they want to be. And laws are written by the powerful elite.
Depending on your views, you might also note that American courts are ruinously expensive and many people are denied access to justice because they can't afford to go through the legal process - which a cheaper parallel system can help with.
Or with different political views, you might note that because the powerful elite get to write the contract, the powerful are only subject to arbitration when they want to be. And laws are written by the powerful elite.