I don't know how to explain it to him any better. I don't want to believe he's messing with us. But I don't know how to proceed without being condescending.
This is the part of the earth that will be facing the sun at the next autumnal equinox (2018):
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365 solar days later (2019), the same part of the world will be facing the sun at the same time.
But it won't be autumnal equinox yet.
The sun will not have crossed the ecliptic yet.
That won't happen for another 5 hrs and 48 mins when the sun is over the Indian Ocean.
A solar year will not have yet transpired at this point when the sun is illuminating this part of the world:
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This is the autumnal equinox in 2019.
This is where the sun will be crossing the equator from north to south in 2019.
Here is where 356.24217 solar days will have passed since the 2018 autumnal equinox.
A new side of the earth will be experiencing solar noon at the equinox.
These images are more accurate than a simplistic diagram/animation that is intended to explain a concept and meant to cause confusion.
These should help anyone having difficulty with this solar year/solar day/equinox relationship comprehend it.