Right, I should have mentioned this is for the US. Here, legal rights are presumptively waivable, even Constitutional ones.

The US also holds certain rights that cannot be signed away, some of which hold for the whole US and some of which are per state. IANAL, but as I understand it the US does allow you to waive your right to pursuing certain types of claims in court (and that waiver can potentially be overturned on a case-by-case basis) but only by allowing arbitration instead. Arbitration is, in the most basic way of speaking, private court with different rules in effect. This is allowed because the US specifically allows it. In fact, the US has generally been a strong advocate of arbitration.

If you can't waive your rights, you can't even settle out of court. That's what a settlement is -- an agreement to waive right to due for some payment.

In the case of basic rights, why would you want to settle out of court?

i.e. if the ice skating rink from the above example is negligent in their requirement to provide a level of care, then they need to be punished by a court.

How is it hard to understand? Settle does not in any way mean "forgive" or "forget" or "waive."

Court: a year (or more) of legal fees, proceedings, headache, stress, and pain in the ass. Settle: Get less cash, be done with it.

In both cases, you're being compensated for the violation of your basic rights. In one of them, you take up the court's time and pay for it dearly in order to make your point publicly and to potentially get more money. In the other, assuming you're trying to sue someone without too much hubris such that they're willing to settle, the affair is much tidier, but generally less bitter for the loser, too.

Why do you have to agree to that before hand? Why doesn't the contract prevent Paypal from suing other parties?