My name is Maximus Decimus Meridius, commander of the Armies of the
North, General of the Felix Legions and loyal servant to the true
emperor, Marcus Aurelius. Father to a murdered son. Husband to a
murdered wife.
With this most iconic of speeches, the Gladiator semantically gave an answer to who he is, and pragmatically, threatened the emperor. The following "And I will have my vengeance" is rather more explicit, but it's not necessary to understand what is being said.
Father to a murdered son. The pragmatic implication here is one of accusation. Commodus had him killed. We and they know that. If that weren't so, it would at most reveal something about Maximus's state of mind. In actual fact, it moves into hostility specifically because it recalls an evil that has been done.
Loyal servant to the true emperor, Marcus Aurelius. The pragmatic implication is one of tribe. Commodus is politically unpopular. He has his guards and such, but there are many on the other side. There is hostility implicit in identifying with the icon of that other side.
General of the Felix Legions. The pragmatic implication here is one of action. As general, he is not some isolated guy on a soap box. He is implicitly a man who inspires action in armies who are personally loyal to him. Speech affects the world, and while semantically Maximus just giving his CV, pragmatically he is calling such armies to join him in open revolt.
My name is Maximus Decimus Meridius. Again, he's just answering the question. But that is the point that you can first see Commodus worry. The key here is context. There is nothing about that sentence as a series of words which conveys anything more serious than "My name is John Smith", but in that context it wraps up everything I've said above. Indeed, the name "Maximus" would soon become a chant, again wrapping up "We're on this side, and you're not."
I should not presume to suggest that this is all that is all that is going on in the scene. It simply illustrates some of the the ways that semantically factual language can indeed be incisive and hostile. I'll swing back to these, but first I wanted briefly to note a few subtle points.
- All of this stuff is hostile. It is not necessarily morally wrong. Of course that's helped by this being a film and Commodus being a creep and regicide being explicitly a-okay. But even in real life, and even when we aren't the villains, opposition isn't automatically evil.
- These examples are deliberately on the more explicit end, which is helpful for illustration. Real world cases are often a lot more vague, and people will often prevaricate on exactly what they mean.
- These statements are all made by one man. At the point that the same things are said by multiple people, the exact implications will necessarily vary. It is polite to assume the best intentions, but it is prudent to be aware that at least some people do not have the best intentions.
Now, why might someone detect hostility in saying that white, all, or indeed black lives matter?
As with Marcus Aurelius, there is a tribal element. BLM is what a certain group says. ALM is what a different group says. For the most part, neither group actually wants to suggest that any lives don't matter. But you nevertheless feel a threat just because the signal is that there are two groups and this isn't yours. Moreover, you probably feel moral offense because at least to some extent you perceive the other group as the bad guys.
As with Meridius Junior, you feel hostility because you feel accused of some wrongdoing. This is perhaps less when Ye West does his WLM stunt because Ye is black. It is in every case a lesser accusation than actual murder! Nevertheless if you're talking to a white guy saying "No, we have to stick with All lives matter" there is an implicit accusation that BLM means his doesn't. You can deny it means that (at least to you, which I'll come back to) but that doesn't stop you feeling the force of his genuine concern for his life and kids and so on.
As with our general, you feel hostility because it is a call to action. I do not mean that it is a call to any sort of violence or destruction, although bad actors associate to all movements. Even at the most gentle political discussion over tea and biscuits, there is disagreement between people who broadly think that racial inequality should be resolved by focusing resources on the typically poorer race, and the others who broadly think that racial inequality should be resolved by supporting everyone who needs help whatever their race. Here the call to action might affect, say, government spending. With that disagreement about who gets what money, there's plenty of room for hostility.
Finally, there is context and slogan, and all the ambiguity that comes with that. Even in the comments on this question, there are people saying that what BLM really means is .... Meanwhile the Black Lives Matter Global Network Foundation is listing demands such as to convict ex-President Donald Trump. That is a plausible political opinion, but it is prima facie a different political opinion from "Police shouldn't arbitrarily shoot black men." There is a similar range of opinion behind all the other statements, although they don't have a convenient demand-making organisation to illustrate the range. In reality, some people saying "All lives matter" will be after an excuse to keep unjust enrichment, while others are just pushing for a broad and consistent politico-legal framework, and others still may want to highly race-specific oppression against other races when that occurs. A lot of the reason that you pick up hostility, then, is that both people from their tribe and yours are arguing different and sometimes odious things under the cover of innocuous slogans. For this reason, slogans make for great rallying cries, and terrible propositional arguments!