Asides the fact that that's provably untrue given I know plenty of people in long term relationships who have no intention of ever getting married, and the wide variety of forms that relationships can take...
Saying "relationships either end in breakups or marriage" isn't untrue, but it's also intentionally misleading and extreme to call a breakup a failure flat-out. Sure, some relationships fail, but others evolve, or the people in them change. It doesn't mean the relationship failed it just means that it ended. And yes, commonly people refer to relationships that didn't work out as "Failed" but that's also, in a lot of ways, directly ignoring what caused those relationships to not work out in the first place. Saying the relationship failed is an easy way to say "It wasn't my fault, it was the relationship."
Also, my "Aunt and Uncle" (Family Friends) have been together for the better part of 40 years, and will never get married or have kids. Why? Because they don't see the point in it when they aren't religious and the law treats them as married anyways, why spend the money? However, to say that because they aren't married "they'll eventually split" is both disingenuous and making a loooot of assumptions about relationships.
Just like there's more to relationships than dates, sex, etc, there's a lot more to relationships than marriage. I respect the people who say they won't date people if they can't see them marrying that person, as that's perfectly valid. However, if getting married is your only goal than you're not dating to find a partner, you're dating to get married, and that's doomed to fail as well.
Point is relationships take a lot of different forms, whether you're monogamous or not, or serious or not. Dating for the sake of Marriage can be just as bad if not worse as dating for the sake of dating. Not only that, but marriage is A: Primarily a religious institution, and B: A legal contract. Nothing more, nothing less, and you can absolutely make a commitment to someone in the long term without getting married.