When to use the gerund?

I was doing this problem from the Barrons 2400 book and I am not quite sure on why the verb tense is incorrect.
“The purpose of the annual career night is illustrating the many professions that high school students may one day choose.”
The book said the verb should be “to illustrate” but why? Can anyone help me?

When a form of “to be” (is, am, was, were, etc.) is used with an ING word, the combined “to be + ING word” creates a verb tense. Like “I am running.” That means the subject - I - am doing the action of the verb - am running.

So right now the sentence is saying that the subject of the sentence - the purpose of the annual career night - is doing the action of the verb - is illustrating. But purposes cannot illustrate things.

If instead we use the infinitive/un-conjugated form, “to illustrate” (a noun when not conjugated), then we are saying the subject of the sentence - the purpose - IS something else, namely, to illustrate. (Much like saying “My dog is a smelly beast.” We are saying the dog IS something else/another noun…a smelly beast.)

That said, the ING vs infinitive choice is a fairly rare error on the SAT Writing MC, particularly presented as to be + ING vs infinitive.