Why do believers of heaven avoid death and/or mourn?
That is a very good question. I'd think that if there is a heaven after this life, they would be anxious to get there! I never quite understood the mourning of those who pass away if you and the deceased are believers. Especially if that person who passed away was experiencing a painful illness prior to dying. You'd think you'd be happy that they no longer have to suffer.
I think most people who mourn are really mourning for themselves and the loss of someone they were close to. I know I would be sad if someone close to me died and I'd never see them again.
I felt that way when my best friend died in 99 from a car accident. Now after almost twenty years it still grieves me (when I sit back and think about it) that he is no longer in my life.
Out of fairness to believers (yeah, I don't know why I bother sometimes, but still) ...
Even IF you believed in the reality of heaven, losing a loved one is still a terrible loss, no different than if YOUR loved one were spirited away to the other side of the planet and you were forbidden to have any contact with them, forever. So while in theory the promise of an eventual reunion in heaven is a bit of a help there, it's cold comfort in the meantime.
The REAL question is why Christians don't commit suicide far more often. Why, in the above scenario, don't more bereaved Christians just join their dead spouse or child in heaven?
It turns out that Christianity DID have a tendency in its early centuries to degenerate into suicide cults, and that is why the curious prohibition against suicide arose. Suicide has been generally considered a terrible sin -- possibly even "the unpardonable sin" that would nullify one's salvation -- throughout most of church history. It is simply an antidote to an unintended consequence of the concept of eternal life. It preserves the carrot with a stick, basically.
Some may doubt you can get to heaven via suicide.
You hit the nail on the head regarding suicide. The church has considered it a sin and the penalty of suicide would be eternity in hell.
Because their reptilian brain does not believe in heaven, it wants to live.
I think it's because the concept of Heaven is born of the same things that make us avoid death and mourn the deceased. It's all a way to deal with the fact that we're going to die. Even with the promise of Heaven, it doesn't eliminate (though somewhat ameliorates) that fear. We are still animals, biologically driven to survive. We have the capacity to think about the reality of death, however, and worry about that inevitable fate which is at odds with our biological imperative. The cheat, then, is to invent a fantasy in which we don't die at all — but I don't think it can fully compensate for the instinctive aversion we have to physical death, even with the hope of metaphysical survival.