This article goes into much more detail. An answer from someone more experienced with this topic may fill in the gaps.
In short, left tackles are asked to protect the quarterback's "blind side," or the side the quarterback is not facing when dropping back (for the right-handed QB, this is the left side).
At one time, pass rushers would rush the quarterback from his blind side. The response to this was to develop a left tackle that can protect the quarterback from the pass rush from his blind side.
Out of the top 101 players in the league before the 2016 season, 0 were right tackles:
Looking at Pro Football Focus' top 101 players in the league, the most highly rated tackles were all protecting their respective quarterbacks' blind sides. Five left tackles were included, as were several guards and even a punter, but zero right tackles made the list.
The article suggests the following:
Part of the discrepancy between right tackle and left tackle
performance can be attributed to the perceived need to have the
stronger player protecting the quarterback's blind side.
Tyron Smith was a right tackle in his rookie season to develop, until the Cowboys moved him over to left tackle after his rookie season.
There's enough data to suggest that quarterbacks rely equally on quality protection from both tackles.
Based on [Pro Football Focus's] 2012 data, pressure from the right side resulted in sacks slightly more often than pressure from the left side. Pressure from the right side ended in a sack 17.3 percent of the time, while pressure from the left culminated in sacks 15.5 percent of the time.
Teams tend to place less talented players at right tackle -- and move more talented right tackles to the left side -- and defenses scheme to take advantage of that weakness. It all contributes to the collective performance deficit at the right tackle position across the NFL.
Pass rushers/defenses tend to challenge the "weaker" side which, according to the quote above, is usually the right side due to the "more talented" tackles playing the left tackle position.