Hey there, ASwissGuy99! I'm a pro lifer. I believe that life is worth living, that the world and the people in it have a lot to offer, and that a better life is possible for, if not all, at least most people. I think that suicide is a tragedy, and I mourn those (my own Aunt included) who lose themselves to it.
With that out of the way, to answer your question...no. No, pro lifers are not right that there's never a reason to give up, choose death, or fall into despair. There are plenty of reasons for these things. We as human beings can only take so much before we break. Many of us really can get better, but will never realistically have the resources and support they need to do so. And some...just don't want to. They're tired, they don't want to go through the pain and struggle it would take to get there, and that's okay.
I think where pro lifers get it wrong is they often turn the subject of suicidality into a moral issue, instead of a human one. Death is always wrong, no matter what. Giving up is selfish and hurts the people who love you. Protecting people from themselves until they can get better is virtuous, no matter what it takes away from them in the process. Letting go makes you a bad person, be it legging go of yourself or of someone dear to you. I think they lose track of the human element, that this is supposed to be about someone else's human suffering, not some kind of ethical imperative.
And also, I think it might be a survival mechanism. You can see this most prominently in people who are struggling to hold on and find meaning in the world themselves. They simply can't accept that holding on may not he worth it, that sometimes things really can't get better, and it'd be unreasonable to expect them to. That for some, death may be the better option. They can't accept this because they want to live in a world where these things are not true. Some of them need these things to not be true, because if they are, it could be true for them. It's existentially terrifying to have to come to grips with the idea that life itself sometimes simply doesn't allow for somebody to be okay, despite anyone's best intentions. For these people, insisting that things can always be better is a coping strategy that they need in order to be okay themselves, and I'm not sure I can really blame them for that. We're all suffering, we're all doing what we feel we need to, consciously or unconsciously, to stave off that suffering, and that's as true for the people fighting against right to die as those who are fighting for it.
I can't excuse the effects it has though. Ironically, the stigma that suicidal people face, that they can't be open about their ideation or their struggles for fear of ostracization, involuntary confinement, or well meaning but no less traumatizing 'interventions' by people who can never truly understand, just creates more suffering and harm. It drives people underground, and cuts them off from the very resources, support, and connections that can actually make things better. The isolation that comes with suicidality (as well as some of its causes, such as depression) can be one of the most painful and miserable things a human being can experience. We are social creatures; we need people. And the fact that people with suicidal thoughts or intentions can't have people in their lives they could openly talk to or commiserate with just exacerbates the suffering that is already there, and prevents the people who do want to recover and whose lives could get better from being able to access or trust the support they need to do so.
I honestly believe that if more people felt they could come out into the open without fear of repercussions or the judgment of society at large, there would be fewer suicides in general. I think people on the pro life side of the argument often forget that.
Honestly, I think what people who are suicidal really need is just some basic compassion and understanding. And this holds true whether they want to recover or they don't. Even someone who's fully committed to catching the bus and ending things at some point deserves to be understood and to feel like people care about them in their final days. Empathy is really the only thing we have at the end of the day to push back against the tide of human suffering in whatever form it takes, and those of us who want there to be less suffering in the world have a self-proscribed duty to extend that. It's really the only thing we can do.
Edit: I just realized my own description of myself means I probably qualify as pro choice, not pro life. Apologies, I'm relatively new to this community and still learning the terminology.