The question of whether to give Abraham a rough or smooth breathing is difficult. Manuscripts differ. We could say that it begins with aleph and that aleph = smooth breathing. The problem with this is that it’s sheer prejudice. We don’t have data which show a regular alignment between aleph and smooth breathing. OK, you say, but rough breathing = aspiration, and we know from lots of languages, the original Hebrew, and the NT versions of Armenian, Coptic, Gothic, Latin, Syriac, etc., that it wasn’t represented by aspiration in those scripts. Fair point, but it still doesn’t settle the question of how it was (a) pronounced in Greek; (b) written by educated scribes.
Look at Liddell and Scott and you’ll see that, if you exclude alpha privatives, ἁβρ- (perhaps with the rough breathing representing Proto-Indoeuropean s) is a more common Greek word beginning than ἀβρ-, so why should Greek not use the rough breathing here and make Abraham sound a little more native?
Now look at some manuscripts for Matthew 1:1 and note the first 12 sources I come across.
B 35 689 690 774 1418 2278 2414 read rough
478 481 1424 read smooth
688 has one of each!
Look at Gal 3:29 and check some different sources as well as some of the same:
B 35 69 104 319 757 2298 read rough
D (06) 1424 read smooth
So it seems that the rough breathing is preponderant. How do we decide which to print? That’s tough, but we know that the accentor of B was really smart and I value him more than the accentor of D (Claromontanus). So with a bit of hesitation, we choose the rough breathing as representing the stronger learned tradition for Greek breathings. Now we’re not thereby saying that anyone ever pronounced this with aspiration. Maybe they did, maybe they didn’t. Nor are we saying that this was pronounced with aspiration at the time of the NT. We’re just saying this: if you’re going to bother having breathings at all, they need to be there to give readers historical information which comes from manuscripts rather than from the heads of editors. Any reader who’s studied Hebrew knows that Abraham’s name in Hebrew begins with an aleph. They don’t need an NT editor to tell them that. What may be of more interest is for them to know that the strongest learned tradition of breathing in Greek is for Abraham to have a rough breathing.
What we’re printing here is not odd or a novelty. It was also what Erasmus printed and other early editions of the TR (which of course were closely based on the manuscripts available at the time). It’s also what you’ll sometimes find, for instance, in Niese’s edition of Josephus that Abraham is Ἅβραμος, given not only the nice Greek ending, but the nice Greek beginning of a rough breathing, in line with the mss.
So in making an edition where we try to model everything we can off the manuscripts we decided on balance to use a rough breathing for this name. It’s not necessarily a big deal, except that users may like to know that thought, care, and above all, documentary evidence has gone into decisions like these.