Why can't an aggregate column also present in group by columns

[niebayes]

This SQL works:

select date_bin(interval 1 day, time) as day, avg(usage_idle) from cpu group by day, usage_idle

However, the following SQL does not work:

select date_bin(interval 1 day, time) as day, avg(usage_idle) from cpu group by day, avg(usage_idle)

It returns an error: Schema error: Schema contains duplicate unqualified field name "avg(cpu.usage_idle)

[niebayes]

I'm also confused about why the usage_idle column can be included in the GROUP BY clause, even if it's already present in the SELECT list.
Some databases seem don't allow this behavior. See: https://www.ibm.com/docs/en/informix-servers/14.10?topic=clause-dependencies-between-group-by-projection-clauses#ids_sqs_1050__title__2

[jayzhan211]

Which statement do you think doesn't allow this?

select date_bin(interval 1 day, time) as day, avg(usage_idle) from cpu group by day, avg(usage_idle)

This doesn't work because the number of rows are different for avg(usage_idle) from cpu group by day and avg(usage_idle). There is no way to represent the result