From http://www.blavatsky.net/judge/arts/ArgumentForReincarnation.htm

IT has been suggested to the PATH that theosophists jot down as they occur any arguments hit upon to support the doctrine of reincarnation. One furnishes this: That the persistency of individual character and attitude of mind seems a strong argument; and adduces the fact that when he was a youth thirty years ago he wrote a letter to himself upon questions about God, nature, and the inner man, and finds now upon re-reading it that it almost exactly expresses his present attitude. Also he thinks that the inner character of each shows itself in early youth, persisting through life; and as each character is different there must have been reincarnation to account for the differences. And that the assertion that differences in character are due to heredity seems to be disposed of by the persistency of essential character, even if, as we know to be the case, scientists did not begin to deny the sufficiency of heredity to account for our differences.

Another writes: If heredity would account for that which, existing in our life, makes us feel that we have lived here before, then the breeding of dogs and horses would show similar great differences as are observed in men. But a high-bred slut will bring forth a litter of pups by a father of equal breed, all exhibiting one character, whereas in the very highest bred families among men it is well known that the children will differ from each other so much that we cannot rely upon the result. Then again, considering the objections raised on ground of heredity, it should not be forgotten that but small attention has been paid to those cases where heredity will not give the explanation.

Inherent differences of character. The great differences in capacity seem to call for reincarnation as the explanation. Notice that the savages have the same brains and bodies as ours, yet not the same character or intelligence; they seem to be unprogressed egos who are unable to make the machine of brain to respond to its highest limit.