My understanding of the Christian objection to suicide hinges on two issues.
Firstly; Life comes from God, and he has put very specific limits on how and when we may take human life - including our own. In a very real sense, as Christians our lives belong to God, and are not our own to dispose of as we like. Historically, the position has been that suicide is "self-murder" . Murder is always a sin, however it is reasonable to suggest that there are degrees of culpability. As has been noted, people who commit suicide are often not fully rational.
Secondly; suicide is inherently selfish. It represents an easy way out of a hard life - whether you believe in heaven, reincarnation (a bum trip if ever I heard of one) or nothingness. While it is hard to interview those who are "serious" about suicide, for by definition, they tend to succeed, interviewing those who desire euthanasia due to incurable disease reveals that fear of pain is rarely the primary motivating factor. Mostly, the primary factor is fear of losing control. I say again, this is a selfish motivation. For a Christian who understands that primary control is in God's hands, suicide is an attempt to take that control away from God,,, and is hardly an act of faith.
When I was "doing the sums" on suicide while depressed, it was these two issues that stopped me.
(1) It did not please God.
(2) It would deeply hurt others.
The positive was that heaven sounded a lot better than this life... but it seems that we have to wait to find out.
Bless all.......... Peter