Hane seki - explanation  

tderz: captures three stones, but also costs a liberty.
In semeais you prefer to start from the outside, resp. taking away the liberties from the other group.
However the left inside the black group form a local seki, hence White is unable to start there.
Thus White puts herself at a disadvantage to start anywhere else than the preferred place (outside/other liberties).
This disadvantage continues after , as White cannot approach from the outside by a, as it would be suicide and create a life-enabling shape for Black.
White is forced to fill another (own) inside liberty -> b.

Hane seki - explanation  

tderz: Now, after Black , White is down to atari c,
but so is Black and thus has to remove the 3 white before playing .

Hane seki - explanation  

tderz: After , White needs to play in order to be able to kill,
however Black is able to play atari and be 1 liberty ahead .

Herman Hiddema: More important is what happens if white does not play in the above diagram!

Hane seki - explanation  

pass, pass

Herman Hiddema: Black continues by filling a liberty at , then capturing at . See the next diagram...

Hane seki - explanation  

Herman Hiddema: White has no option but to play , to keep the black group dead. This doesn't help however, as black now plays , putting the white group in atari.

The above diagrams are the true reason that neither player should capture in the original diagram. At the start, both players have a big eye. By capturing you remove your own big eye. See also BigEyeSmallEye

Hane seki - wrong starting position  

tderz: The position started as here and White had to find a way to survive (play h).

blubb: Why doesn't White play at the marked point? ^[1]

Hane seki - verification  

tderz: Replying to blubb's question Why not to capture at
After ,

• White has sente and 4 liberties (1 outside + 2 inside + 1 shared inside liberty = 4 in total),
  
• Black only has 4 liberties (1 shared liberty + 3 inside liberties (5 for the yon-nakade are reduced to 3 as Black is forced to created sanmoku nakade by a necessary capturing move in gote) = 4 in total)

Hane seki - variation  

tderz: After black becomes necessary, as is .
Black loses by 1 liberty (2 : 3).