Which one is correct?
- I met my future wife on this very American traditional occasion.
- I met my future wife during this very American traditional occasion.
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During is an unusual preposition in that it can only have an object that refers to a duration of Time -- there are fewer than ten words in English that have exclusive time reference, and many of them come from the same root as during. It is also unusual in that it's almost never metaphorical. Objects of during will be interpreted as temporal references:
Occasionally one must strain to interpret them that way in context:
That's the problem with using during with occasion as its object. Which temporal part of the "occasion"? The dinner, the visiting, the travelling, or what? Occasion normally refers to a notation on a calendar -- a 2-Dimensional metaphor -- rather than something with a temporal duration of its own.
On, on the other hand, requires some two-dimensional surface as an object, and produces a location that is above and in contact with that surface:
but on is more usually metaphorical, and will work with anything that can be metaphorized to such a surface, which includes just about anything:
The last example shows how we use all three Spatial dimensions to refer to Time in English. In general,
That's why on is better for occasion.
Both sentences are grammatical. There are two differences in usage, though slight.
A traditional occasion is presumed, by definition, to be a recurring event. You may have met your future wife on the occurrence of the event, many years ago, or last month. It may have been in Omaha, just as likely as in Guam.
The second sentence,
is more readily understood as a particular instance of the occasion. Both time and location are associated with specificity. So "during this occasion", would more likely imply "last month in Guam" versus "decades ago in Omaha", for example.
I was surprised though, that "on" and "during" seem to be used interchangeably when I checked just now. The most common English language usages of "on the occasion of" were in Indian (Hindu, Muslim and Sikh) wedding invitations. There was merely one traditional Roman Catholic wedding guide that I found. It used "on the occasion of". Even a wedding announcement posted in the informal venue of the Yahoo! Groups Geophysics forum used "on the occasion of"! I am personally most familiar with American English, and Jewish wedding invitations. They use "on the occasion of".
Regarding more general usage of "on the occasion of", whether weddings or commemoration of formal events, Fatwa Online and Defender of Sunna use "on the occasion of" (all English language websites). Also, Fatwa Online makes the distinction that "on the occasion of" refers to the general case of the occasion, rather than a specific instance, to which I alluded to above.