Are you suggesting that we kill the children in the system because they are unwanted?
Of course not, because the thought of murdering innocent children, or even just condoning the murder of innocent children would horrify you (I assume), even if you don't have the means/desire to care for them yourself.
The fundamental disagreement here is when it becomes a human life, not whether or not we, as a society, care about children. There is nothing transformative that happens at birth. In fact, neither of my children were even born, they were simply cut out of me (c-section). They are still both, very much, my children. He could have cut them out a few days earlier or a few days later and it would not have changed the fact that they were human infants, not just clumps of cells.
We, also, are often not discussing the same period of development when arguing this issue. Having an elective abortion in the first trimester is a far cry from having an elective abortion in the last trimester, yet these are often lumped together in the same argument.