The Offers and Demands option seems to be for recording demands received from counter parties, but it is possible to record a demand that your company has made to a counter party.

The demands/offers come from people/companies listed in Parties/Entities, so you can certainly create a demand from 'you' to someone else.  While the verbiage is "Demand From" and "Offer to", you could select "Demand From", then select your own Entity as making a demand of some other Party/Entity.