'suicidal’ was short hand for very depressed and thinking that would be the easiest way out. He’s not drinking heavily or on the verge of overdose. He’s just really really low and needs a friend.
I think you said 'suicidal' when you thought it would make people think maybe he should stay with you.
Then you backtracked because people reacted telling you how unbelievably responsible it would be to have someone suicidal staying in your home against your children's wishes especially when one already has behaviour problems bless him.
I've been suicidal. It's awful, truly truly awful. Although you now say he's not suicidal because people agreed (quite rightly IMO) that it makes your judgement on this even worse.
So people aren't being unsympathetic to him if he's feeling so low. But he absolutely should not be staying at yours - your responsibility is with your children. Do you really think any child, especially one already struggling with behavioural problems, will be able to feel settled, safe and parented with a suicidal friend of their mum staying?
And you say 3-4 days... what were you planning to do on day 4 when he says he still has nowhere to go and if you kick him out he doesn't know what he'll do etc?
FYI from someone who has been suicidal a number of times, 3-4 days doesn't make any difference in the long term. It's not anywhere near long enough to wade through your issues.
If he needs housing he also needs to presenting as genuinely homeless so you won't be helping on that front either.
FFS, your poor kids having this to worry about.