tl;dr Because I say so.
No? Well, I have two perspectives on why you should try out paleo (strict, no cheats, for at least 30 days).
The evolutionary angle:Humans are primates. The primates diverged from the other mammals approx. 50-85 million years ago. But if you go to the zoo or look up primates in a encyclopaedia you will notice that their diets are all pretty similar. Primates are omnivores that eat leaves, fruits, stems, flowers, tree sap, and animals, both invertebrate and vertebrate, as large as they can catch them. Only the gelada are exclusively vegetarian and only the tarsiers are exclusively carnivorous (yeah, I am totally lifting all of this off of Wikipedia). Anyway, the point is that anyone who claims that humans are originally vegetarian or carnivorous are wrong. The great apes to which we belong have some interesting adaptations to the main components of their diets though: Gorillas have sort of bubbles on their colons to ferment some of the large amount of fiber they eat and orangutans are able to remember where all the fruit trees in the jungle are and when they have ripe fruit (but yeah, omnivores). And humans are able to digest meat and complex carbohydrates from roots and tubers more efficiently by cooking them. This increase in calories then allowed us to develop larger brains which made us more efficient at getting food. Vicious cycle, this sentience business is. And whether early man were hunters or scavengers is completely irrelevant - both are efficient strategies. And this has probably been going on the last two million years, since human ancestors developed long limbs and became the heat dissipating champion of the mammals.
Okay, so we've talked about primates and therefore humans being omnivores. Isn't this how modern man eats today (the majority anyway)? Well, no. The majority of human calories today come from the seeds of grasses and legumes, from extracted simple carbohydrates, and bovine milk products. And we live on this and we procreate but we could thrive better. Why not seeds? There is a thing called Red Queen Hypothesis that states that a host and parasite must both continually evolve to maintain the balance of their relationship (after the Red Queen race in Through the Looking Glass (Alice in Wonderland) where they run as much as they can without getting anywhere - Lewis Carroll was obviously making a comment on the futility of treadmills and cardio workouts). For grasses and legumes the seed is an enormous energy investment and the plants that put in defences are more successful than those that don't. The mice and what else lives on those seeds and beans then have to evolve to dodge those defences. We are new-comers to the grain eating business and while some of us are well-adapted, others are very poorly adapted (like celiacs) and most of us are somewhere in between those two extremes. The same goes for dairy (and I'm not just talking about lactose tolerance). So what about all the other plant matter that people on paleo eat? And why are animals okay - wouldn't it be in their interest not to be eaten? Okay, one question at a time. Fruits are a mechanism for spreading seeds far so there has been co-evolution of plants and animals towards the same goal: Healthy animals and more of that plant. Same goes for nuts. Squirrels forget ~25% of the nuts they hide away. So the tree is sacrificing some of it's "babies" so that the others will have success. For some plants having poisonous leaves is a viable strategy while for others it clearly isn't. It is easier to understand why if we look at animals though. For prey and predator there exists a symbiotic rather than parasitic relationship. Sick members of the prey species are killed and removed so they can't infect others. The predators keep the number of animals down so their food sources have time to grow and replenish itself. And monitoring of herbivores on islands with no predators confirm this - the population numbers vary wildly which both reduces the genetic diversity of the group by putting it through several bottlenecks but also puts it in danger of extinction. So while a predator is bad news for an individual it is a good thing for the species as a whole. Some poisonous animals do exist however - but this is always in very rich ecosystems with many many species. For plants sacrificing some leaves means that an animal could poop out some nutrients from a plant it ate somewhere else. It evens out the uneven distribution of trace elements. There are more factors but just know that for some plants and animals there are advantages to being eaten and for some there aren't.
tl;dr Humans are omnivores. For some plants and animals there are advantages to being eaten and for some there are advantages to not being eaten.
The other angle:It works. Eating after a paleo pattern addresses most of the hypotheses behind the global obesity epidemic and the diseases that follow with the foods that make folks fat (yeah, just because you aren't fat doesn't mean that you're fine - sorry mate). People feel, look, and perform better. They heal things that wouldn't go away previously. They are less miserable (ever tried a calorie restricted diet? No wonder people are miserable). And it's fucking delicious.
tl;dr it's awesome