We do know what to. He said, "I was late to meet my friends."
And it doesn't matter how important what he was late to was, unless you can prove some sort of gross negligence or that he was intentionally harmed.
It starts from, "Would a reasonable person believe that a [less-than-taxi] ride sharing service has guaranteed arrival time?" So even without considering the terms of service, we can already easily arrive at, no, a reasonable person would know that a ride service, even a real taxi, does not guarantee arrival times. And indeed, an arrival time is never even negotiated. So any harm that is caused by his being late rests on his own shoulders; cars sometimes get flat tires. It can be expected that a car has a chance to get a flat tire, even a hired car. It doesn't matter what the harm is unless you can prove that it is the fault of the driver or ride company.
You certainly never would have a person on the side of "there is no liability for that" having to brainstorm theories of harm. The person asserting liability has to do that. Be default there is no liability; some reason has to be provable.
A jury is going to be very upset at having their time wasted by somebody claiming that they didn't know part of hiring a car was that the car might get a flat tire, be stuck in traffic, or otherwise break down or be late. It is a known and obvious part of transportation by automobile. It is going to be difficult even to keep a straight face while claiming, "I never knew it was possible for a hired car to get a flat tire, and now that I know, I blame the driver. The driver certainly must have known that the car can get a flat tire, and negligently didn't maintain the tire properly." See how much fail there is there? To make it the drivers fault, it has to be both totally unknown to a reasonable consumer that there is a risk of flat tire, and also so well known to the driver that failure to prevent it is not only negligent, but grossly negligent. And in a ride-share, the driver is claimed to be an amateur just "sharing" a ride, not a professional taxi driver, so it rapidly gets more and more stupid. This is all long before you need to worry about what he was late for with his friends.
Compare that to rape. It is almost exactly the opposite; you'll have a hard time convincing a jury that being raped by a company representative is a normal risk that you would anticipate as part of the service. How do you even make the claim? "She should have known that being a woman and leaving the house, she might get raped." The jury isn't going to be in a good mood.
The defense for a taxi company is that the industry is regulated, the risk is regulated, and the local government decides on granting the driver a taxi license or not, and so the company has followed the system. It isn't their fault, primarily because the regulation establish the standard of how much checking they are supposed to do. So it is hard to make a free-form, "didn't do enough" type of argument. Without complying with that regulation, Uber doesn't have any of that protection. They can't hide behind the government. And if the plaintiff can show they made a minor mistake or oversight, or that they could have done better, or that some particular rapist would not have received a taxi license, well then they might win a giant lawsuit.