Don't take away your own liberties

 

White has taken territory and Black some influence. It is tempting to reduce White's territory by pushing at a.

 

However, after , Black's liberties are reduced from six to five.
As his formation is still open to invasion, reduction or attack, losing a liberty is too high a cost compared to White's cost of 1 point at this stage.

Furthermore, this move loses a ko-threat, but that was not the issue here.

Before  

White's stone has four liberties.

After  

A vain attempt to cut the bamboo joint: White's stones now have three liberties.
This will always be bad (exception if played as a ko threat)

White disregards liberties  

The exchange - leaves White with three liberties: the same number as she had before. This is one of the ideas behind hane at the head.

White gains liberties  

After here, whatever Black does, she (White) will end up with at least four liberties for her group.

A bad push  

Black pushes at to create weaknesses, but...

if black doesn't defend, then white can kill  

...because of shortage of liberties, he can no longer play a to make a second eye

White disregards liberties but cuts  

tderz: if White's intention is to cut at either or a, then this might be the (only) way.

if the surroundings allow  

tderz: The exchange - leaves White with three liberties: the same number as she had before. This is one of the ideas behind hane at the head. -> if the surroundings allow and the situation fits, Black may be cut & in a bad/worse situation, as both only have 2 liberties.

White gains liberties  

tderz: this is espec. good & important if the direction , is the route for escape/attack.

sente & a perfect wall  

tderz: is sente once game is about 11 points/move (23/2) and Black needs to defend with .

reverse sente (1)  

tderz: Black's push at can thus also be considered as a good reverse sente,
as it creates a weaknesses (of course, Black has to come back and defend).
Continuations could be a-b-c-d-e or c-(f, h or i) etc.

reverse sente (2)  

tderz: perhaps the goup is heavy now and on the left there are imponderabilities as a + b + c.
I certainly prefer defects in opponent's wall + split groups in gote over
being forced to accept a perfect wall in gote.