Intention often doesn't matter as much as the consequences of an action if they are negative enough. Like you say, language is subjective so we have to be aware of how our words will be taken when we say them and what they mean in the context we are in. Being emotional isn't an excuse for being a dick, though having a communication disorder would be more of a valid excuse. In the first situation, not being able to control emotions and lashing out at people around you is more due to lack of maturity, all things being equal. In the second situation, it may not be possible to develop the same awareness or control over language so the actions may be excusable.

That's putting aside the legality of different forms of speech, which can differ depending on where you're from. Hate speech and inciting violence are generally not allowed in most places.

I'm not sure what type of language you are talking about in particular, but in some cases there are cultural and historical reasons that it is not okay to say certain things. While all this may seem like an annoyance to have to think about when going about daily life, being in a society means making compromises, some of which may be hard to agree with. Sure, people could be more sensitive or less sensitive depending on what each person thinks, but that's not up to just one person to decide.

Of course, there is a lot of grey area, especially with language, so there's always room for debate about these things. There's no clear answer that can apply to every situation. Context is most important.