While I agree that the 'N' word is something I would not use, and personally think it's been considered offensive for long enough now that most people of working age should understand why it would be better censored, I think it's a slippery slope to assume that EVERYONE is entirely up to date with the correct vocabulary for all instances and that making one mistake deserves the most severe punishment. I'm in my 30s and within the last few years have experienced various acquaintances (colleagues/friends/family), all of whom I would consider to be nice, fairly well educated people in their 20s-60s, not those who would ever want to hurt feelings or deliberately use the wrong terms, say things like 'coloured people' 'transsexual' 'retarded' (describing something rather than someone), etc.
My organisation considers itself to be very up to date on terminology but atm still uses BaME which I know some of my colleagues strongly dislike, so I could absolutely imagine if I, for example, went on maternity and was away for a year, or transferred to a different job, could use what I thought to be the 'correct' phrase but be wrong.
The correct reaction the first time someone says the 'wrong' word, particularly a trainer, whose whole job is to educate, should be to say something like 'I'm sure you didn't mean to cause harm but that term is considered to be out of date and offensive, most people now tend to use the term xxxx/if we can all avoid saying the full word during this session. Thanks! Now to answer your question....'
A decent person would then apologise and know for the future, and it would also have the benefit of educating everyone else in the session/nearby.
Not go 0-100 in sacking someone for what is likely to be an honest mistake. If the guy had been warned before for something similar that would be different, but doesn't seem to be the case.