Well, personally, I am against abortion. I feel that, from the moment the child is conceived, it is a living person, and therefore abortion is murder. The only time I would condone it would be in cases of rape or abuse, but otherwise, I just think it's a huge no.
As for your question, I don't feel that the father should be allowed to do that. Whether or not it was accidental, the child in question is still his child; giving him the option to back out with a financial abortion is basically just saying it's okay for him to be a "deadbeat dad". As someone mentioned earlier, the father being lied to about the mother being on birth control would be a difficult issue, because the father would assume that there was no possible way for him to get her pregnant, particularly if he was using protection as well. In a seriously unlucky scenario where the condom ripped and the birth control was ineffective, then i'm not entirely sure, because it's really nobody's fault in that case.
However, if it was simply one or the other, ie. him using protection OR her using birth control, and something went wrong and she got pregnant, he should have to pay for the child, because they weren't as safe as they could be. Additionally, if neither of them used any sort of protection, then in my opinion, the father should have to pay extra for the child just because he was dumb enough to have sex without it, particularly because he knew the implications of such a choice, be it pregnancy or STDs.
I just don't feel that the father should really have a choice in the matter. It was his fault that she's pregnant, he doesn't have to carry the child around for 9 months, and he doesn't necessarily have to adjust his life to make room for the baby. There's also the chance that the mother mightn't want the baby either, in which case, abortion is completely out of the question, in my opinion. I personally know a couple who absolutely adore kids but are unable to have any of their own. People who get pregnant accidentally and abort the child are just selfish, because that child could easily be put up for adoption and make another couple seriously happy.
That's just my take on it though
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