According to Sarek's wife, Amanda, the disagreement between Sarek and Spock over Spock's career choice in Starfleet, rather than attending the Vulcan Science Academy, stemmed from Sarek's wish that his son follow his teachings, as Sarek had followed those of his own father. (TOS: "Journey to Babel")
Background information Edit
This character was only mentioned in dialogue.
In Star Trek III: The Search for Spock, Sarek's family line is given – the line states, "Sarek, child of Skon, child of Solkar." This is normal for many cultures even on Earth – to list one's direct ancestors in this manner. Sarek is the child of Skon, who is the child of Solkar, and so on. Following the traditional Vulcan name nomenclature, Skon should be male, and thus, Sarek's father.
There were plans for Skon to make an appearance in the unproduced fifth season of Star Trek: Enterprise. He was also a principal character in the aborted film Star Trek: The Beginning, set in 2159, as the Vulcan ambassador to Earth.  In the first draft script of that film, Skon was described as "a wise and distinguished-looking Vulcan."
According to the Star Trek Customizable Card Game, Solkar, father of Skon, was the Vulcan captain who greeted Zefram Cochrane in Star Trek: First Contact. The mirror universe counterpart of this Vulcan was killed in 2063. If that Vulcan was actually Solkar, this would indicate the Skons in both universes were born in or prior to 2063.
Skon's wife is named "T'Rama (β)" in the short story "A Girl for Every Star". In the Thirteenth UK Story Arc, Spock had a cousin named Horek (β). This implies that Skon had another child besides Sarek, one of Horek's parents.
In the Star Trek: Deep Space Nine novel The Lives of Dax, Skon is portrayed as a mathematician temporarily aboard the USS Heisenberg. He was friends with Tobin Dax, but was not impressed by his magic tricks. The Star Trek: Enterprise - The Romulan War novels Beneath the Raptor's Wing and To Brave the Storm feature Skon and Tobin working on United Earth's Warp Seven Program during the Earth-Romulan War. The novels likewise depict them as being close friends, as does the subsequent Rise of the Federation novel A Choice of Futures.