What's the weather forecast for tomorrow? What does the weather forecast say about tomorrow? Shouldn't for be used here to represent ownership?

(Indicate the object, purpose, etc. ) here, right, here?

Used to indicate who is going to own or use something or where something is going to be put.

There is a letter for you. There is a letter for you.

This is a children's book. This is a children's book.

We bought a new table for the dining room. We added a new table to the dining room.

This is my favorite place. This suits me very well.

about

Belong to (something); Part of (something); About (something)?

Belong to sth; Become a part of sth; Be related to sth

The lid of the box. Lid

A director of a company.

A member of the team. A team member.

The outcome of the debate

Excerpt from Oxford Dictionary

It is not difficult to see that of is more subordinate, while for is functional "for, for, about"; So when you say tomorrow's forecast, you mean more "tomorrow's weather forecast (broadcast on the news, the forecast content has little to do with tomorrow, just that the broadcast time is tomorrow)"; Tomorrow's forecast is "Tomorrow's Weather Forecast".

Yesterday's prediction of yesterday was wrong; It didn't rain at all yesterday! The weather forecast was inaccurate yesterday. It didn't rain at all yesterday!