By the same reasoning, given that men are mortal, and everyone will die eventually, why have any doctors at all?
At the very least, the refusal of one doctor gives the unborn baby some additional time to live. Perhaps that is just an hour or a half, but even that is more than nothing.
And yes, the physical results are not all that matter. Yes, “keeping his own hands clean” is also good (by the way, no argument to the contrary has been cited here).
And that looks like a dishonest argument.
If he claims that such an action makes no difference, then why should this action be forbidden? And if this action does make a difference, then why does he argue that it doesn’t?
So, he claims that refusal doesn’t matter, because a different doctor will promptly perform abortion - and that it must be forbidden, because that “other doctor” isn’t actually available?
It is obvious that he is not right in both cases. And he needs them both to be true for his argument.
Not much of a surprise here - after all, anything follows from a contradiction.