The majority of people do seem to think that behaviour is manipulative, but I honestly disagree with their assessment. When you care about someone a lot, then they say they're going to leave your life forever and never contact you again, of course you are going to experience intense emotional pain, similar to grief.
This can push someone to the brink of suicide, especially if they only had a meager amount of people in their life to begin with, only to lose a crucial supporting figure suddenly. Suffering a loss is a big driver for suicidality in many people, it does not mean that someone is malicious, manipulative, attention seeking, lying, and so on and so forth for them to voice how deep that pain has cut them.
I think people might view these words as maleficent or ill intentioned becase the default belief in our society is that expressing suicidality in the context of another person's actions is akin to making a serious threat against them. A lot of people characterise talking about suicide as an action done for strategic/persuasive purposes, i.e. one has something to gain, like making a partner stay with them so the other party wouldn't harbor the guilt of feeling responsible for a suicide.
In reality, lots of people are simply being honest that ending up in a worse situation due to someone's else's decisions does makes them feel MORE suicidal, and you are not playing mind games like the majority thinks. While it is a very unpopular stance to take, I don't think expressing one's pain like this is bad behavior. However, as I mentioned before, many people will not see eye to eye with you and me on this, so if you want to discuss these topics you have to sort of censor and hold back your true feelings.
Instead of telling someone the lack of their specific company makes you feel more suicidal, it is more productive to say that loneliness or isolation heightens those emotions. People don't like to feel responsible for the wellbeing of others, as unfortunate as that fact is, so if they are told directly that their presence is vital for your happiness, it might be too much for some individuals to bear.
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