None of these things are wrong or irrational:
a) Have the police called on a suicidal person. b) Have the police arrive armed ready for violence if the suicidal person is armed. c) Have the police demand the dropping of the knife with clarity and extreme defensiveness/precaution. d) Shoot the knife-wielding man if he did indeed charge at them.
The reasons why:
a) and b) People here are criticizing why police even show up at all for a call like this. "They're not qualified to deal with mental health cases," and such. That is partially true, and their are better ideals for people we could have handle these situations. But in the real material world right now, suicidal people can be dangerous (especially if they're armed, like this case), and it does make more sense to have the Police, who are equipped to handle and contain a violent/belligerent/psychotic/unpredictable suicidal person. The key word is unpredictable. The lives of the people called to respond to the situation matter, and the lives of the other people in the environment matter too (the girlfriend, in this case). Police are called because the essence of someone who is acting crazed/drunk/psychotic is unpredictability and you want to control the risk.
c) To minimize the risk of violence, the dude has got to let go of the knife. Whether the officers had tazers, handguns, rifles, batons, whatever, it is not worth getting too close to the suicidal person. If he doesn't cooperate, they're left in a stalemate with big risks for either course of action they can take (either stand back and risk letting him proceed with hitting himself before they can get close enough to get the knife themselves, or move in and risk being stabbed).
d) If someone's coming at you with a knife, you can shoot them. A Tazer would be ideal, but have you ever seen someone not be deterred by a Tazer? It happens, and especially when the target is not sober and/or psychotic. While not psychotic, the knife-wielder does sound like he was hysterical and also clearly not sober. So in a closed space like the room the cops went up to to handle this situation, and the unpredictability of the problem awaiting them, guns are not out of proportion.
It's an awful situation all around, and I'm not trying to take away from that. Every component is awful: a guy wanting to end his life. A girlfriend losing her loved one. An amount of protection and force that is justified in theory but probably wrongly applied in this case. The douche cop's Facebook comments that undermine everything I'm saying.
It's a shitty situation, but the immediate conclusion-making by so many commenters here is not necessary. Instead of looking at this as "typical bad-guy police" and "man wow the cops are assholes" or "omg why do police show up for suicides at all", it's really just a fuckup. There are a lot of sound practices that were employed here, it just went to shit.