It was advertised as "The Feel-Good Film of the Decade", actually, thanks to a bonkers review from the News of the World's Robbie Collin. You can't blame Danny Boyle for that, although the distributors should have known better. The whole "feel-good film" nonsense was frequently and strongly criticised by Mayo and Kermode on Five Live, and has become synonymous on that show with any film that's depressing or uncomfortable viewing.
The BBFC classification of 15 is explained thus:
SLUMDOG MILLIONAIRE is a drama about a young street lad who wins the Mumbai version of 'Who Wants to be a Millionaire'. It has been classified '15' for strong language and violence.
The film is in a mixture of English, and subtitled Hindi. Together with several uses of strong language in English, there are also a number of untranslated uses of strong Hindi terms - all of which were considered acceptable under the BBFC Guidelines at '15', which permit 'frequent use of strong language (eg 'f**k').
Strong violence is seen in a scene where a group of Muslims are attacked and killed in the street - together with general chaos and beatings, there are some stronger and more explicit moments, such as the deliberate setting of a man on fire, that go beyond the BBFC Guidelines at '12A', which direct 'Violence must not dwell on detail. There should be no emphasis on injuries or blood'. We also later see strong violence that includes a knife held to a woman's throat as she's forcibly snatched off the street, an impressionistic blinding of a young beggar boy, and torture by electricity in a police station.
So in their view 15 is appropriate for the content. Don't forget that 15 doesn't mean that it's a film aimed at 15 year-olRAB, but that it's considered unsuitable (and forbidden) for under-15s to watch. There are plenty of PG and 12A films that aren't intended for 12 year-olRAB, but they don't contain any content that's unacceptable in that classification so that's the category into which they fall.