In a sentence like "He is taller than me", the word 'than' is used as a comparative and is considered a conjunction. Thus, you use the subjective pronoun rather than the objective.
Examples:
"We are taller than them", is really saying "We are taller than them are tall". Does that sound correct? Nien.
The correct way of saying that is: "We are taller than they", as it is really saying "We are taller than they are tall".
When you use 'than', mentally insert what comes after the pronoun to see if it makes sense.
Correct:
"He is taller than I am tall"
"He is fatter than she is fat"
"She is smarter than he is smart"
"I like playing video games more than she likes playing video games"
Incorrect:
"He is taller than me am tall"
"He is fatter than her is fat"
"She is smarter than him is smart"
"I like playing video games more than her likes playing video games"