It's tough sometimes, isn't it? That's a question I've struggled with, too. I'm not sure which stories you're referring to, but are you thinking of instances like the story of Noah or Joshua in the Bible? Where God chose to take the lives of people who were choosing to disobey? Or are you talking about other (ie polytheistic) legends of different gods who were fallible, passionate and vengeful?
I can't speak for other faiths, but my God, the one we read about in the Bible, sometimes chose to take human life.
That does seem counter-intuitive at first- if God loves all of his children, why would he do such things?
Before addressing that, kind of a tangent. The last thing you mentioned- proof. A very valid question- how do we know that God even exists? The answer is deceptively simple- just ask Him. And then wait. He will answer. When I say that, I'm not trying to be a know-it-all or give a textbook answer. It's a hard-fought, hard prayed answer I've received for myself, and its very special to me.
Back to the initial thought; for what it's worth:
Life is sacred, and no-one has a deeper rooted love and respect for life than God. As life's creator, he has a pure understanding of life's meaning and purpose. That purpose is to come to earth and have this experience, in which we feel love and hurt, joy and misery, anger and peace. We grow in maturity and prepare to return to God, where even greater tasks and purposes await.
Life is not merely existence, and death is not the only way to destroy life. Interfering with the purpose and direction of a human life on earth can have consequences that last into the next life. When man destroys life in this way, God cannot sit idly by
There is a scripture in the Bible that says words to the effect of "God does not delight to punish the wicked, but rather delights in those who repent"
Just as we can die both physically or spiritually, so can we be injured spiritually or physically. One form of spiritual injury is sin. When we make a mistake, God wants to help us. He wants to heal us, and so he will help us work through that hurt. Sometimes, however, people refuse to be healed, refuse to change, and worse, cause other people to hurt themselves. God sends warnings to stop. When these warnings are ignored soon lives are destroyed, spiritually. The destruction spreads, hurting more and more people. At times, there have been entire groups of people that have behaved in such a way. As much as God loved them and did not want to destroy them, he had to protect his other children. If he did not take action at such times, even more lives would be destroyed, and in a deeper, more profound sense than the death we think of.
I agree wholeheartedly with you, death IS part of life, but it is not the last part. Nor is birth the first part. Death, I think, is too often misunderstood- it is not the destruction of a being or soul, but rather an emergence from a cocoon into a higher life.