As is stands, parents are able to claim their children as dependents on their tax returns, which lowers their overall tax liability and in effect means that the parents either pay less in taxes or receive a higher return at the end of each year.
Until they reach the age at which they can work, children are a drain on society. They receive public schooling and receive the same benefit from public services that adults do, yet they contribute nothing in return. At the point that they reach maturity and are gainfully employed and paying taxes, they become a functioning member of society.
If a parent decides to have a child, they are making a conscious decision to produce another human being. They could choose to get a sterilization surgery, use birth control, or abort the pregnancy (assuming they don't live in a backwards state that's banned it). Yet even if they decide to have 15 children, the rest of society has to foot the bill for their poor decisions until the child reaches adulthood.
By increasing taxes on parents instead of reducing them, you not only incentivize safe sex and abortion, but you shift the burden of raising a child solely to the individuals who are responsible for the fact that that child exists.
I am a strong advocate for social programs: Single-payer healthcare, welfare programs, low-income housing, etc, but for adults who in turn contribute what they can. A child should only be supported by the individuals who created it.
I would say the problem is not in taxing, it's in the school system. Kids used to start working at 14, now they study until 30. You have "adults" that are basically still children from tax perspective. We need less school (the stuff we learn, not to ever use it in life again...) and more work.
I don't really have a problem with adults that study until they're 30, as long as they come out of school being an expert in a field that's actually useful to society. A medical student just out of high school who goes into pre-med, medical school, then residency will be close to that age by the time they finish their education. Somebody who hops from major to major and eventually gets a degree in philosophy when they're 30... maybe find something that's actually useful first. If you're working and contributing and decide you want to study art history for your own personal edification, go for it.
The world is vastly more complex than it ever was before. I get it feels useless, but learning anything makes us smarter.
Being smarter means we will handle situations intelligently. There is no useless learning.