Huge difference and you aren't seeing it. I'll try again.
If you cut yourself, that's on you. Nothing I can do will stop you, so harm minimisation training is the least-worst option to minimise what you do to yourself.
If you tell me to cut you, that's on me. You cannot consent to me cutting you. I'm not a regulated medical professional carrying surgery, I'm an ordinary joe, and if I cut you it will be ABH. You cannot consent to ABH. I am morally and legally obliged to refuse. Harm minimisation training doesn't even come into it because I shouldn't be cutting you at all.
The same applies to strangulation. You could be crying and begging for me to strangle you and it wouldn't make the only acceptable answer I can give be anything other than "oh hell no".
Strangling someone isn't an act of self-harm, it's an act of harming someone else, that's literally the point. It is never OK for a man to strangle a woman. Men are not obliged to commit crimes if a woman tells them to and it's misandry to claim that men lack the agency to do the right thing and the judgement to know what the right thing to do is. The women asking to be strangled are vulnerable, as all people who wish for harm are, and they need the true protection of men saying no to strangling them.