To the best of my understanding. I am doing this as an attempt to articulate the ideas and see where my knowledge base needs improvement. The premises, will be followed by the argument and then possibly some examples/thought experiments. If you feel that anything is missing, unstated, or unclear; please comment so I may clarify.
Some traits breed true (inheritance)
Children are not exactly like their parents (variation)
Children are somewhat like their parents (inheritance)
If a creature dies before it can reproduce it wont have children
Not all creatures of the same "type" are identical (variation)
If none of a type of creature successfully breeds, we call this extinction.
If one variation of a "type" of creature is more successful (in breeding) than another variation then more of the next generation will resemble it.
Existing generations are replaced by their offspring (survival) or not at all (extinction).