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I'm not a teacher
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In this particular example it seems it's just a matter of collocation.
Interestingly enough, you use the formula with "have
a something" when the pleasure of the subject and no particular purpose are involved
(that's not the only way you use the structure though) e.g.
1. I had a walk/ stroll/ swim.

2. I had a walk
to my friend's place.
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It might be pleasurable for the subject (you), but it serves a purpose - you want to reach your friend's place, it has a destination point
3. Every weekend we had a walk
around the pond.
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You can say 'where' but not for what purpose
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P.S. You can find more information on this and similar structures in
The Semantics of Grammar by Anna Wierzbicka. The chapter's titled
Why you can have a drink when you can't *have an eat.