What is the reason that tertiary alcohol pKa is higher than primary alcohol pKa?
The short answer is that the steric hindrance of the tert butyl alcohol makes it hard to add an protonate the hydroxy group.

Based on this lecture from the vanderbilt university. The answer is due to steric hindrance:



The hydroxy group of the tert butyl alcohol is intramolecular stabilized by hydrogen bonds (2nd image), between the methyl hydrogens and the oxygen. In the other hand, i.e. the hydroxy group of methanol is intermolecular stabilized with another methanol molecules (&quot;Behave more like a water&quot;) (3th image). Therefore, the equilibrium $\ce{ROH}\rightleftharpoons\ce{RO^-}+\ce{H^+}$ is more displaced to the right with the methanol than with the tert-butil alcohol.
 

The protonation of ter butyl alcohol is slower than methanol (Figure 4th and 5th), for the same reason: steric hindrance.