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 never suggest that children or adults should live in poverty. As long as someone is doing a job to the best of their ability, they should at least make a living wage, and I would gladly pay higher taxes or an increased cost on goods to help support that.
What I am suggesting is producing a child is ultimately a personal choice made by the parents, and they should foot the bill associated with their choice. If someone can't afford a child, they should not have a child (and the rest of us should help pay for birth control or abortion). If someone has a child that they can't afford, the child should be removed from the household and given to a family that is both willing and financially able to support a child. If that's not an option, the child should be placed in a state-funded care center and given an education and basic necessities until they become an adult. The ultimate goal is for adults to think twice about reproducing unless they are fully capable of raising a child on their own and for a large number of people to stop having children.