Does the father have to pay child support if he opposes the birth?

Yes. He didn't complain when it went in, so he can't complain when it comes out.
MY OPINION. Is the man so shallow to think that he can do what ever he wants and have no responsibilities? It sounds like he believes that abortion is an option. He wants the easy way out (for him only). Sexual intercourse has it's risks and one of them is a possible pregnancy. Suck it up and help support the child. I am a father and would do anything for any of my children.  
Legally he is obliged to pay child support for any child he fathers but on that note i believe if he is not on the birth certificate (has not parental rights) he is not oblidged to pay child support (or have rights to access to the child either). You could legally write up an agreement between the mother and the father for child support instead of going through the agency as an option. And your child support should be apportioned to how often you care for your child.
Please note: Dont let people make judgment on your child custody/ support case as everyone is in a different boat. I personally believe both sides have a say in contraception so both are at fault if pregnancy occurs and i believe both should have a say in what happens if pregnancy occurs but it seems in this day and age the female rules completely. If she wants a child she will have one. I am a female and have seen both sides of the story many times and am sick of the way fathers get treated most of the time (yes there are exceptions to every case). To cut a story short child support is the law and although sometimes the law doesn't look so balanced we must all obey to make the world as balances as possible. Unfortunately the world is grey and the law is often seen in black and white,