It is a fact that humans are able to de-humanize each other. This is bad.
But that is not an argument or reason for anthropomorphizing every inanimate object. And if you want to draw the line somewhere, so that only some inanimate objects are people, then we have to argue about where to draw the line. The "but slavery..." argument only deals with actual humans, so it doesn't tell us that LLMs also get to be considered to be people.
Human slaves are embodied, and have a continuous consciousness from birth to death. LLMS have no bodies, cannot meaningfully be killed (to erase one is analogous to it leaving a particular location... it can still be in many other locations at the same time), do not experience pain, do not have emotions, and do not experience time (when you ask one a question it wakes up for a moment and then goes to "sleep" again after replying to you). You can't even meaningfully identify an LLM as an individual, since it was trained on the collective utterances of all humanity, and any little change to it makes it a different entity.