Picture. Why would archery be a pre-condition to mathematics? Why would the wheel come before horseback riding? Why would currency be as late as in the medieval era? I don't understand. Is this really the best they can make of a historical game?
Well, I am not sure if this one can be answered outside of guessing what was the intent of the game developers, but our very own /u/restricteddata wrote about Civilization for an academic journal before and here is an interesting discussion where he talks about it. Hope it helps a little, it is certainly interesting.
If we take the Civ tech tree to be implied to be more than just a game mechanic (in which choices allow different types of upgrades in different sequence), it makes for terrible history. It is true that in many cases, there are technological "prerequisites" and going down one "path" has led people to various kinds of new outcomes. You cannot really end up with nuclear weapons, for example, unless people are studying atomic theory, particle physics, and radioactivity — these concepts are necessary before the idea of nuclear weapons will even appear.
Several things are muddled about the Civ tech tree, however, as any kind of actual historical "map." For one thing, for obvious reasons there is nothing like simultaneous work — your science output gets applied to a single idea at a time. Obviously real history does not work that way, even when states have directed resources to specific problems. For another, as I've written in [a review](http://alexwellerstein.com/publications/wellerstein_reviewciv6(endeavour).pdf), it's pretty unclear what the historical mechanism is here. Nobody "researched" archery — it was a technology that arose, seemingly independently, in many different places of the world. In fact, the idea of researching technology with science is something that doesn't really happen for most of human civilization (and putting science and technology into the same "tree" is something of a historical anachronism — they typically evolved quite separately).
The actual ordering is itself not quite right in many places, and it is a pseudo-Eurocentric approach to these things anyway (engineering, the compass, gunpowder, and education predates the medieval era by a significant fraction of time if you look at the Chinese view of things). Some of these linkages are totally bonkers — why does biology get you oil? Why do you need dynamite (patented in 1867 in the real world) to develop the rail road (Stephenson's "rocket" was first developed in 1814)? Why do you need lasers (first working one demonstrated in 1960) to get the hydrogen bomb (first detonated in 1952)? Well, the answer here is game balance (the real world is not very "balanced" — as I note in my review, if the real world was a game, nukes would be totally OP and would need to be nerfed by the developers, the fact that a couple of nations could go from kilotons to megatons in less than a decade is just totally unfair), not history.
Which is a fine excuse as long as nobody confuses this with how history works. Unfortunately many people do make that confusion and do think that Civ teaches you "about history," which it does in only the most superficial way. Because Civ does have pretensions to this, and wraps itself with historical tropes, I do think it opens itself up to these kinds of criticisms (whereas StarCraft does not, because nobody thinks it is meant to "model" anything). At best, Civ is a strategy game wrapped in a thin veneer of history. You could imagine a Civ-like game that had something like a tech tree that more appropriately modeled history (it would have far more contingency to it — different civilizations develop different things in different orders, and without any foreknowledge of what it would necessarily lead to!), but it would be a different game, potentially not fun.
The Civ tech tree should not be considered a factual way to look into actual theory; it's called gameplay and story segregation, and it's an especially important consideration in games based on history.
Take for example games based on WW1. If you want it to be especially realistic, you'll probably be spending most of the time dealing with lice and trench feet, which won't make for an exciting game. So liberties have to be made.
As an aside, if you're wondering how to rationalize the tech tree, take a gander at this r/civ thread.