We are not talking about a "family" but talking about government, that is something very different and it is very dangerous to view government as a "family" in the same way it dangerous to view a corporations or your employer as "family"
To treat people differently you would have to start basing income tax rates on characteristics of a person, such as race, sexual identity, age or height (like in your previous analogy)
Saying all income from 0-50000 is tax X, and income from 50000-100000 is taxed Y is not treating PEOPLE differently, all PEOPLE are treated the same in that situation.
To be clear I am a supporter of replacing all Welfare programs with a Negative Income Tax. I would also be in favor of a UBI that was not funded with Income taxation.
I also support the abolishment of all Income based taxation replacing it with Georgism Single Tax System
Characteristics like their marriage status, the number of children they have, the status of their home, their status as a student, or even the specific example you used of age which is tied to all sorts of taxation issues?
Although I'm not sure there is any point to continuing the conversation if you are going to nitpick any analogy and refuse to recognize that your views on taxation are an extreme minority opinion.
Meanness and unfairness are two different things.
Especially in a family setting, sometimes niceness can Trump fairness.
Sometimes fairness means leveling the playing field so everyone can compete equally.