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 don't have kids and I take the train. I still pay taxes to build schools and roads because I know we're going to need SOME of them one day. While I am hugely biased toward the idea of massively-dense islands of housing and services, to cut down on maintenance (and use of) roads, keeping transportation medium and education targets and goals in the hands of voters - an idea that is only barely better than every alternative - allows for direction and guidance later (through voting).
We fund the things we need to keep within our control, should we ever wake up and exert that control.