It's not that easy thinking of all the other humans as really being people. There are so very many of us, and not all of us are like you. Many of us believe incomprehensible things, behave in baffling ways, feel strange and foreign feelings. So that's part of the reason we tend not to think of each other as fully human: it actually takes some effort to get our heads around how much there is that makes us fundamentally much the same, when there is so much that makes us obviously different. Our ancestors never had to deal with the idea that there were billions of other creatures with comparable experiences, emotions and needs to themselves; there was never much call to extend their circle of compassion much beyond their immediate tribe, who were unlikely to number more than a few dozen - a hundred or so at most.
There is a plausible theory which suggests that our brains simply aren't equipped for relating to more than a certain number of other people - this figure, known as 'Dunbar's Number', is probably somewhere between 100 and 300. It's a small step from there to the idea that we can't fully appreciate the humanity of many more people than that. This is the theory of the Monkeysphere, and I think it helps make sense of a lot of human behaviour, but that's not really what I want to talk about here.
If it's innately quite difficult for us to see all the other humans as people, it's not surprising that it can be quite easy for us to see people as other than human when it's convenient. Equally, it makes sense that we are susceptible to being manipulated into seeing other people as less than human by parties with something to gain from that. There are quite a few dimensions to this - demonization and objectification are full-on varieties of dehumanization; medicalization, exoticization and stereotyping can have strongly dehumanizing effects, when people are seen as collections of symptoms or other characteristics, rather than fully-rounded individuals with their own motivations, pleasures and foibles. There is something deeply dehumanizing about many institutions, too, and perhaps any big organization; where people are able to avoid actually engaging with those they have power over, and some measure of efficiency is officially supposed to take precedence over human relations anyway, it is no surprise when folk stop treating each other as people. Depending on how you feel about the measures of efficiency used in such contexts, you may or may not think this is a bad thing.
It is clear that demonization is a stock tool of those who wish to wage war, in any form, for any reason. Convince your population, and especially your army, that The Enemy is evil, wrong and just generally demonic, and it's very much easier to persuade them that it's okay to massacre them. Those pushing for war, or just looking for a scapegoat to distract attention from the real causes of problems, routinely downplay the humanity of The Enemy, and amplify the differences in their moral outlook. Grievances are ignored, justified anger is painted as inexplicable hatred. They hate us because we're wonderful! Those monsters. They must be stopped, at any cost! So it goes.
If we accept that dehumanization plays a part in many of the evils that beset humanity, is there anything we ought do about it? Is there any hope of us individually and collectively respecting the personhood of six billion homo sapiens, let alone the various other species with some claim to personhood? It's not really clear, but there are a few things that might help. One is being on the lookout for politicians and the media demonizing and otherwise painting anyone as less than human, particularly when they have something to gain from it. We should try to notice, too, when we find it convenient to see others only in terms of their physical appearance or group memberships, in relationships and arguments. Another strategy is to try to keep things organised on a human scale whenever possible, so that nobody is lording it over people they've never really interacted with, and will never see as anything much more than a statistic or a small collection of salient facts. To do that would mean resisting the centralizing tendencies of both capitalism and statism, and probably abandoning certain economies of scale. We might also need to stop allowing our economy to be dominated by structures which compel people to put aside their own humanity, let alone anybody else's, to prioritize the kind of efficiency that can be easily quantified in monetary terms. Maybe this is all hopelessly unrealistic, but I don't think we know that yet; the status quo is far too often mistaken for the natural order of things, and many things stay broken but unchanged only because people have forgotten about trying to fix them.