Getting back to the OP's question:
Well I'll start with the most basic premise - that defenses want to attack the blind side of the QB with their best pass rusher.
That's worth quoting.
Most quarterbacks are right-handed, which means that not only are most left tackles defending their blind side, but most offenses (read: non-NFL offenses, which are more sophisticated) are set up with a bias to the right side of the field.
The traditional Pro set offense has an end tight on the right side of the line, with a flanker split wide, a single end split wide left, and the quarterback under center. This bias happens because it is easier for a right-handed quarterback to read the right side of the field during his dropback then the left side, hence why the strong side is set that way.
It is also simpler from a footwork perspective to make handoffs that way, especially stretch handoffs; if you watch high school and college games, you'll note that sometimes those handoffs gets botched and the quarterback has to run the ball because he wasn't quick enough getting to his spot. That's especially common if the stretch is to the QB's non-handed side. So that's another reason why the tight end is usually set up on the right side.
So in the lower levels of football, left tackles are usually on the blindside of the QB, are usually unsupported by a tight end, and are often matched against the defense's best pass rusher. This arrangement tends to incubate pass blocking skills.
This leads to a left tackle bias on the pro level because to switch sides, a college left tackle turned right tackle has to relearn all their footwork. While NFL offenses do their best to eliminate bias to confuse the defense, for this reason you still have a significant difference between right and left tackle on the pro level; along with the previously stated reason that most quarterbacks are still right-handed and the left side is the blind side where the best down rusher is.
Thus, left tackles on all levels are valued for their pass blocking abilities; long arms, agility, balance, speed, etc. Right tackles tend to be like the rest of the line, powerful inline blockers with strong leg drive. Those requirements change quite a bit depending on if you're primarily a passing or running offense.