Married couples have different tax treatments because of community property rules, and because the unit of taxation is the household, rather than the earner. It would be rather regressive to tax a two-person household each earning $25k/yr at the same rate as a single individual making $50k/yr, despite the fact that household income is the same. The intent of the different treatment of married-filing-jointly returns is to attempt to balance the tax paid by married couples so that it's roughly in line with the taxes that would be paid by individuals filing separately. This may result in tax benefits or penalties depending on the earnings status of each of the spouses, but it's hardly an across-the-board. "Tax divorces" are a thing; high-income couples may find it financially advantageous to divorce (even if they continue to live together as a de facto married couple).
As far as kids being an "advantage in their financial livelihoods"...well, yeah, that's just hilarious. Kids are expensive. Tax breaks for kids are a progressive measure intended to make it slightly easier to afford to provide for one if you're in the lower echelons of the economy. If you think that anyone is having kids because of the financial advantages they convey, you're high.
Regarding the article, the "financial benefit" isn't from being married, it's from not being a dependent of your parents. There's no married person favoritism at play here; it's simple dependent eligibility status. You can achieve the same thing by being 24 years old, or by being legally emancipated.