Why do identical twins sometimes have noticeably different personalities?
The short answer: identical genes don't mean identical lives, and personality is shaped by both.
Twin studies have been the workhorse of behavioural genetics for decades. The consensus from large studies (the Minnesota Twin Family Study is the most-cited): personality traits are roughly 40 to 60% heritable. The remaining 40 to 60% is environmental - but here is the crucial bit, most of that environmental variation is "non-shared" environment, not "shared" environment.
What that means in practice: even twins raised in the same household have very different experiences. One twin gets the math teacher who notices her. The other doesn't. One twin breaks an arm at age 9 and develops a cautious streak. The other doesn't. Multiply this by 18 years of childhood and you get two genetically identical people whose personalities diverge in ways that look surprising from the outside.
The field used to assume that "shared environment" (the family) was the big environmental driver. The data forced a revision. Family explains less than people thought. Individual life events explain more.
Quick reality check on the genes-aren't-everything point: identical twins also aren't quite genetically identical at the cellular level.
Mutations happen during cell division. By the time twins are adults, each has accumulated hundreds of somatic mutations that the other doesn't carry. These are usually trivial, but they add up. And gene expression - which genes are turned on or off in which cells - diverges significantly through life because of epigenetic changes driven by diet, stress, illness, environment.
So "identical twins" is shorthand. The DNA they were born with was identical. The DNA they're walking around with at 40 is close but not the same. And the patterns of gene expression - which is what actually translates DNA into biology - can differ a lot.