Suicide out of desperation - loss of friends, loss of house, family, job, caught cheating, etc. This is suicide of free will. This is desperation.
We should never be that desperate. It is a lack of trust in the Lord. We trust that God WILL take care of us. No matter how bad it seems now, things WILL turn around, maybe later than sooner, but, they will. Perhaps God wants us to learn something from this experience. Perhaps God wants someone else to learn something from our experience. There are many reasons bad things happen - and often they are because of our own actions....that we don't see, until it's too late.
Therefore, this form of suicide is cowardly and just an "easy out". It's terrible that someone reaches this point. It breaks our heart. However, there's nothing we can do at this point, other than pray for them. They can no longer repent for this last action of theirs. They can't go to confession and get absolution. This is a terrible way to finish your life.
This is not judgmental of these people. It's sad they get to this point. We need to keep our eyes open and help EVERYONE, because we don't know how sad, desperate, deflated they may be. This is why we should never belittle, humiliate or degrade anyone!
As for the sick, who take their lives. It's still an "easy" (although, in truth difficult) way out. Nobody wants to suffer. However, perhaps through their suffering they come closer to God before they die. Perhaps their loved ones come closer to God before they die. Perhaps it affords an opportunity for others to do good deeds towards this person, and bring them closer to God. There is always a reason.
Only God knows...and we need to trust Him - always. In good times and bad.
As was mentioned, not all suicide is considered "suicide" by the Church. These things are investigated, and those people who were not conscious of their actions and the results of their actions, will not be held accountable. It's like holding a baby who rolled out of the 10th story window and died, responsible for his own death.
The Church is kind and loving. Don't think it's not. It give the benefit of the doubt, however, it's up to us to help each other and give each other support, not cut each other down all the time.
Even on this forum, some folks think it's funny to tease and belittle. However, few of us really know the person we are teasing, and what situation they find themselves in. They may be at their ropes end and our snarky comments might just do them in. Therefore, always be nice to each other.