Why can’t this be solved using a Venn diagram? When should I use the method used in the solution rather than a Venn diagram?
This is a bit tricky. The reason a Venn diagram doesn't work here is because we're discussing two different types of people (men and women) with two different attributes (tenured and untenured). The Venn diagram works when attributes or types can be shared across "circles".
For example, let's say I have a Venn diagram with a circle containing attributes A and a circle containing attributes B. They overlap, and in the middle is the intersection. That area has both attributes A and B. This would make sense if we were talking about hair color and eye color. It doesn't make sense if we're talking about men and women, since there is no overlap.
So the real question you should be asking yourself when deciding on the diagram used in the solution vs Venn diagram is if the attributes are overlapping. Of course, you could always attempt to draw it out and see whether or not the logic of the Venn diagram holds.
Anyway, I definitely recommend you watch the related lesson videos when you're stumped on a method. The double matrix method lesson video will help you get a better idea of when to use the method used in the problem.