Good catch. However the (US) Supreme Court has held that arbitration clauses can be invalidated which is why most companies here either offer the ability to opt out of arbitration, burying the language where almost no one sees it, or exempt small claims court. This accomplishes their goal of avoiding class action lawsuits while greatly reducing the risk the arbitration clause be held to be unenforceable.

BA has not only failed to do this but placed the arbitration language under subscriptions so its not even clear the clause applies to purchases.