Unfortunately, this issue has long been defined by the feminists as one of "choice", not responsibility. Or an issue of "their body" (certainly not an issue of reproductive rights, or of life or death). So if we're going to look at this issue in terms of responsibility, particularly for men, then consider:
In stark contrast to women (and choice), men have no choice whatsoever. None. Zip. Nada too. In our society, all of the reproductive decision making power resides in the female. Men get no veto, no vote... no rights whatsoever. And without rights, responsibility is difficult to impose- perhaps even unjust.
What if we changed these rules so that men had both greater rights, and greater responsibilities?
What if men had a vote in the birth of their child? If a man voted yes, and a woman voted no - the man would be responsible for raising the child. (and vice versa)
And if the man voted no, he also would know of his own personal responsibility.
Maybe, just maybe a baby would be saved.