I don't see how that would work. If a teenager or college student gets the UBI they can still outcompete the breadwinner, unless the UBI is enough to provide... but why wouldn't they just stay home and raise their kids or provide care to their elderly parents etc?

They absolutely could do that, which is the point. UBI gives you the freedom to make the best decision regarding how to use your time. If UBI is enough to cover you, then spending time at home raising kids and taking care of your family may be the best use of your time, which is a win for both your family and society.

Both of those things provide value to society as a whole. Raising children that will grow up and be part of society has value. Taking care of those that have difficulty caring for themselves has value. Both those things have additional value in having people doing it that are emotionally connected, and not strangers doing it for a paycheck to have their basic needs met. Allowing people to be able to do those tasks and still meet their basic needs is good for everyone. It also takes pressure off the job market, where basically every single person needs a job. Companies could more freely automate low paying low skill jobs without having to worry about what happens to those people that would be “put out of work”.