I have to agree with RandomAngel; [He didn't say "Don't tell anyone"; at most he implied "Don't tell Tara [right now]."]
It sounded like Arnold was being asked why he left Ben so that Tara could pull parallels on why her ex might have left her. Temporarily ignoring the fact that every couple is different and as such, so would be reasons for breaking up, but Arnold, reasonably, didn't want to plant the idea that hey, maybe Tara's ex was cheating on her and that's (also) why Ex left. So he didn't tell her, at the time.
If you look at the timeline, 'late 2012' Arnold broke up with Ben and in 'early 2013' Tara and Ex split, so that's probably only a couple months between them? So it's reasonable that Arnold might still be talking about his breakup and such with friends at that time, but now it's a year later, so naturally the subject isn't going to be coming up anymore. These friends apparently tell each other everything(?), but go months without interacting, just picking things up where they left off when they get together again. It seems logical that the subject never came up again with Tara. So this bit of information just fell through the cracks.
As such, I don't think you need to apologize. But, since Arnold volunteered the information to you, I would consider just being equally frank with him, that 'hey, this happened, so it's fresh in Tara's mind now/she might be angry with you." Or however it seemed like she was taking it at the time. Given the space between meetups, Tara could have digested the news by then and it won't be awkward. I would look at parallels between Bill & Arnold to help guide you.. were they at the same status in the group/with Tara before they cheated? How does Tara treat Bill now? etc.