In "Pinky and the Brain", a simple observer can see a clear pattern: Pinky's antics are the cause of most of Brain's failures.
If Brain is so smart, why doesn't he just do an analysis to remove Pinky, to finally succeed in world domination?
In "Pinky and the Brain", a simple observer can see a clear pattern: Pinky's antics are the cause of most of Brain's failures.
If Brain is so smart, why doesn't he just do an analysis to remove Pinky, to finally succeed in world domination?
This is partly answered by the fact that, for all his bumbling, the Brain clearly considers Pinky to be his best friend and partner-in-crime and wants them to take over the world together - on occasions where Pinky is in danger, Brain drops everything to save him.
The rest is addressed by the episode "That Smarts". Brain comes to the same conclusion as you - that Pinky is the cause of his constant failures - but rather than ditch him, he opts to increase Pinky's intelligence so that it's on par with his own. The newly-intelligent Pinky proceeds to point out that a lot of the time, Brain's plans actually just have some kind of flaw that cause them to fall apart on their own. This is reflected in the show: Brain's plans are accidentally foiled by Pinky some of the time, but other times they just flat-out don't work.
The Brain, being an arrogant, self-righteous, socially-awkward control freak, exhibits this lack of humility most likely due to a deeply rooted insecurity and lack of self confidence. This could be due to one of many causes.
Perhaps his ratling peers made fun of him and shunned him from social groups for appearing physically different from others as a juvenile rat on account of his macrocephaly. Perhaps he was weaned from his mother rat prematurely. Maybe he was left unattended with a weird rat uncle far too often despite his pleading because his financially unstable family couldn't refuse the monetary compensation that came with the arrangement.
Whichever traumatic reason left the emotional void in his soul, The Brain has an insatiable desire to feel noticed, to feel powerful and therefore respected, and to prove his worthiness that presented in controlling behaviour and self-centeredness with delusions of grandeur leading to a relentless urge to takeover the world among other unhealthy defense mechanisms designed to keep his ego overinflated in a desperate attempt to have it protect his atrophied self-confidence.
Pinkie essentially serves as The Brain's outlet for angst and fulfills his unconscious need to appear "better than". Without Pinkie to accentuate his intelligence by comparison, The Brain would likely fall into a deep depression. Additionally, Pinkie's neuro-simplicity makes The Brain feel needed and therefore useful and worthy.
Essentially, Pinkie and The Brain's co-dependent relationship is what gives Pinkie the overconfidence to maintain his pursuit of world-domination which, ironically, if achieved would leave The Brain without a purpose any longer and therefore Pinkie's unintentional foiling of their nightly mission is also essential to The Brain's vitality.