Skype does not give you the option to go offline to a specific contact. Instead, you have to go offline to all contacts to avoid being seen by that specific person. The only way you can appear offline to a single person and remain online to other people is to block the person. Then, unblock the contact if you want to appear online again to him. The person is not warned in any way when you block him, but you won't be able to receive any of his messages until you unblock him.

Block the Contact

Locate the person you want to block. To quickly locate the contact, type her name and press "Enter." Click the contact to display the conversation window and then right-click anywhere in the window and choose "Block This Person" from the context menu to display the Block Contact dialog box. If you want to remove the contact from your People list, check the "Remove from people" box. To report the contact to Skype, check the "Report as spam" box. Click "Block" to block the contact. You go offline to the contact as soon as you click the "Block" button.