Why can't you mix Aggregate values and Non-Aggregate values in a single SELECT?

Question

I know that if you have one aggregate function in a SELECT statement, then all the other values in the statement must be either aggregate functions, or listed in a GROUP BY

Answer 1

The aggregate function and the group by clause aren't separate things, they're parts of the same thing that appear in different places in the query. If you wish to aggregate on a column, you must say what function to use for aggregation; if you wish to have an aggregation function, it has to be applied over some column.