Some says it's forbidden to show images of living creatures. The argument is this hadith:
Ibn ‘Abbaas (may Allaah be pleased with him), who said, “I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say: ‘Whoever makes an image in this world will be told to breathe the soul into it on the Day of Resurrection, and he will never be able to do that.’” (Narrated by al-Bukhaari and Muslim). He [Ibn ‘Abbaas (may Allaah be pleased with him)] also narrated that the Prophet (peace and blessings of Allaah be upon him) said: “Every image-maker will be in the Fire, and every image that he made will be made to appear to him and will torment him in Hell.” Ibn ‘Abbaas said: “If you must do that, then make trees and things that have no soul.” (Narrated by al-Bukhaari and Muslim).
There are also some that says it's permitted, depending on the intentions. The argument is the hadits below.
Narrated A’ishah: When the Apostle of Allah (Peace and blessings be upon him) arrived after the expedition to Tabuk or Khaybar (the narrator is doubtful), the draught raised an end of a curtain which was hung in front of her store-room, revealing some dolls which belonged to her. He asked: What is this? She replied: My dolls. Among them he saw a horse with wings made of rags, and asked: What is this I see among them? She replied: A horse. He asked: What is this that it has on it? She replied: Two wings. He asked: A horse with two wings? She replied: Have you not heard that Solomon had horses with wings? She said: Thereupon the Apostle of Allah (Peace and blessings be upon him) laughed so heartily that I could see his molar teeth. [Abu Dawud]
Rasulullah SAW(PBUH) permitted Aisha to play with the dolls. He even laughed - which could be interpreted a symbol of agreement.
The different views on this matter is not yet settled. However, what categorized as 'living' is objects that live, and able to think - Which includes humans and animals. The paintings of trees, landscapes and abstract paintings are not in this category. So regardless whether painting living things are allowed or not, a skull is not in this category. Therefore, it's not Haram. However, the most important part of an act is the intentions. If one intent to worship the skull, then it goes straight to the Haram, forbidden category. Else, if it's just for decoration or maybe you have a t-shirt with that drawing, Insha Allah it's Halal.
I think what makes your father uneasy is the fact that a skull is very closely related to 'dark' acts. It's scary, it's used in pagan rituals and the list goes on. For this matter, it's up to you, since it depends on your intentions, why do you like that shape. Well, personally i would advise you to just show some respects to your father - he isn't wrong to be uneasy.
Here is some external sources:
http://www.youtube.com/watch?v=rFd-SUP3Two - Dr Zakir Naik.
Wallahu a'lam. And Allah knows best.