Well looking at the global situation, we see that White's bottom right group is pretty solid and White also has a 4-4 on the left side. The first observation gives a good reason why 'a' would be the most played move because it's a defensive move that makes it more difficult for White to utilize her solid bottom group to make profit on the right side. The second observation explains why the 2-space high pincer may not be such a great candidate:
And a running fight occurs.
works especially well with the 4-4 because it attacks 
and supports the 4-4 at the same time. There is the a-c joseki, but it's naive to expect White to play like that in such a global situation. So why is 'i' more popular than the two-space high?Perhaps because its low placement allows Black to settle more easily (a stone on the 3rd line is, in general, easier to settle and live than a stone on the 4th line, which has more access to the center). Of course, White could try to play similarly and get a running fight:
The crucial difference is that White's running group doesn't have as many options for making base (compare the availability of L18 in the last two diagrams).
Note: These are just my own observations and not from what I've picked up in pro commentary/analysis, so I could be very wrong here (especially since I'm writing this at 5am)...but hopefully it makes sense.
I should also mention that Yilun Yang's "Whole Board Thinking in Joseki" Vol. 1 and 2 are essential when it comes to answering questions like these.
Secondly, I never saw the counter pincer. It looks too sweet in relation to the left 4-4 and must be prevented!