Great stuff from Mary Beard:
Apologies are always difficult. There's always a fine path between the Scylla and Charybdis of saying too little and saying too much (do we really need to know...?. Then there's the question of whether you seem sincere or just mouthing it. There's hundreds of times we've heard people say "I am very sorry if I upset you over this" (carefully not, "I am very sorry to have done this"): good enough or not?
In a way, too much scrutiny of the words is perhaps beside the point. Apologies are rituals, they are a very simple case of "doing things with words". The only thing that actually counts is the audible expression of "I'm sorry" (like "I do" at a wedding). Or are we expecting people to SHOW contrition? And how do we recognise it, in any case. Some people can seem dead truculent and controlled but actually be eaten up inside -- and vice versa.(...)
I particularly dislike the governmental kind which fulsomely apologise for some dreadful wrong of the past (like slavery or our treatment of the Maori -- or, in the case of the Pope, the death of Galileo). It's not that those things are not terrible wrongs, but a government apology seems too easy a way out. It has all the appearance of a "that's OK then" line being drawn under the issue, and a pretty low cost one too. (Rather like "First Capital Connect apologises for the late running of this train and any inconvenience caused".)