SELECT AVG(age) FROM persons HAVING age >= 18

is incorrect because having clause can only be used with fields specified in GROUP BY clause or aggregate operators' results.

SELECT AVG(age) FROM persons WHERE age >= 18 GROUP BY name

will return average age of people with the same name.

SELECT AVG(age) FROM persons HAVING AVG(age) >= 18

will be executed without errors, but will return a completely different ersult