A family of Microsoft relational database management systems designed for ease of use.
It appears you are heading in the right direction, but you have put some speed bumps in your way.
The Main form should be bound to the School table only. It should only have controls bound to fields in the School Table, plus the subform controls.
When dealing with subforms, I always design the subform separately, then use the subform wizard to embed the existing form on the main form.
I would create the Sports subform using the Form wizard. I would add the Sports field first, then the SchoolID and the Junction table ID (Note I name my PKs tablenameID to make them easily identifiable). Use a tablular layout for form. Then go directly into modifying the form. When you change the textbox control to a combobox, you have to fill in the properties. You have to set a Rowsource, Bound Column, Column Count and Column Widths as a bare minimum. It might be easier delete the textbox control and use the combobox wizard.
You refer to the "record source" of the Sports combo, but combos have a RowSource, not a recordsource. And the SQL Statement you show is incorrect. The RowSource should be:
SELECT SportID, SportName FROM Sports ORDER BY SportName;
(Note: Name is a reserved word in Access and shouldn't be used for an object name. And I wouldn't just use the default ID name for the PK).
I would then Set the Visible property for the ID and SchoolID to No, so the subform only shows the Sport Combo.
For the Deliverables, I'm not sure I'm following what Offered is. If the Deliverable is specific to a Sport, then the SportID should be a foreign key.