Its hard to say or deny such statement as "humans are self-destructive by nature".

What does mean to be self-destructive? Being self-destructive to yourself or to others, be able to be self-destructive, or something else?

Beside that its always hard to take the lines on some patterns - for instance if you take some individuals and want to make assumptions on all human beings.

Did you read I'm OK, you're OK by Thomas A Harris MD ?

I believe, as long as human is able to control and reprogram mind, and come up with certain absolute moral facts, it is definitely not self-destructive being.