If my response interests you, I suggest that you read up on Derrida's later ethical thought. This is a decent introduction: https://iep.utm.edu/derrida/
My response to your question is that I don't think we can 'justify' either using birth control or not using birth control; I think we simply do it. To decide securely in favour of either choice entails an appeal to metaphysics - usually, an idea about the value of life, which collapses under closer scrutiny.
In the decision to have or not have a child, either choice requires us to consider our responsibility to the others who will be affected; we fail to meet some of our responsibilities to others in either choice that we make.
I think these questions, and many like them, are beyond rationalistic ethics, and are decided on the terrain of power and desire.