Okay, so we start by beginning with intent of free expression. Free expression protects everything you say with the exclusion of you harming others. That's a key intent of freedom in the US, as long as you don't hurt others, you're okay to have freedom. And so many people don't even understand this, which is a sad part.

So, with this information, we have a case where a girl tells her boyfriend to commit suicide. Just by using pure deduction, she was an accessory to a crime, suicide. But this case is much deeper than that.

The reason to why it's manslaughter and not murder/accessory to murder is because she hasn't actually killed him. She did drive him to suicide with his words, but that does not mean it's murder. She did not help murder anyone so it doesn't work. But the reason to why it's manslaughter is because she did kill someone. Manslaughters legal definition actually covers unintentional killing as well, where you take participation in due to negligence. That's why there's such charges as vehicular manslaughter, etc. (Or, why people get charged with manslaughter when they accidentally kill someone due to negligence of construction material, firearms, etc.).

One could point to the fact that it's murder because she kept on persuading him to kill himself, it's clearly premeditated. But in the end, he's the one to make the decision, which is where you are right. But the issue becomes the fact that she knew he was going to kill himself and just told him to do it.

That's why it's manslaughter. She didn't murder him or order the murder of him. It's manslaughter because she was completely negligent, persuaded a mentally ill person to commit suicide. Could there be a crime made for this? Sure. But it'd be completely niche. It'd be better off as manslaughter.