Why are the secondary alpha hydrogens more acidic than primary alpha hydrogens (keto-enol tautomerization)? I learned in organic chemistry that secondary/tertiary carbanions are less stable than primary carbanions and therefore primary hydrogens are MORE acidic than secondary/tertiary hydrogens.

But lets take 3-methyl-2-butanone as an example. It seems that the more substituted alpha carbon is more acidic than the nearby primary carbon. In other words, it seems that the keto-enol tautomerization prefers to form a C=C with the secondary carbon over the primary carbon.

Why would a base prefer to deprotonate the secondary carbon over the primary carbon to trigger keto-enol tautomerization over the theoretically more acidic primary carbon?
You're actually asking two questions. There is both kinetic and thermodynamic acidity. There are times when performing deprotonation at low temperature will yield the kinetically favored conjugate base, i.e., the proton that is most exposed. If you increase the temperature of this intermediate, you can get to the point where proton transfers happen in reaction vessel to create the more stable thermodynamically favored conjugate base. Usually, this is the more substituted one.