Riot police put out a fire in Kiev as they surround protesters in Independence Square. (YouTube)

Tens of thousands of protesters returned to Independence Square in the Ukrainian capital of Kiev this weekend, two months after demonstrations against the president first began. They're not as large as the initial clashes, which protested President Viktor Yanukovych's decision to reject a deal for closer integration with the European Union. But they show that Ukraine's crisis is far from over. Here are three reasons the protests came back.

First, President Yanukovych signed a new law limiting basic freedoms.

Nothing gets activists back out in the street like signing a law that imposes strict limits on the press, on peaceful assemblies, on Internet use and even on speech itself. Some Ukrainians are calling it "the law on dictatorship" and it's not hard to see why.

Second, Yanukovych's government is seen as drawing closer to Russia.

Russian President Vladimir Putin capped off a year of foreign policy successes by offering Ukraine economic stimulus worth $15 billion and giving the country a 33 percent discount on Russian natural gas. The political crisis was in many ways over whether Ukraine would lean more toward Moscow or toward Europe – a dilemma it's been facing, and to some degree putting off, for its 23 years of independence. This certainly does not mean that Ukraine has annexed itself to Russia, but for Ukrainians who would rather their country turn west than east, this was one of several recent indications that Yanukovych is going in the opposite direction. Tellingly, they've also criticized the new anti-protest law by calling it Russian.

Third, the core problems driving the protests are all still there.

Ukraine's politics have long been divided into two major factions by the country's demographics. What's happening right now is in many ways a product of that division, which has never really been reconciled. Just about every Ukrainian government since independence has been seen as representing one "side" of this divide, with the other hating him or her as a perceived foreign pawn. That's exacerbated by political corruption and by the fact that Ukraine's troubled economy does indeed make it reliant on outside countries. Today, Ukraine is still demographically divided, its government is still troubled by corruption and its economy is still in bad shape. As long as those things are all true, public unrest is likely to continue.

One big caveat is that, while all of these factors are problems, not all of them are necessarily unpopular with all Ukrainians. After two months of protests, many Ukrainians are tired of the public demonstrations and would like to see a return to normalcy – something that also happened in Egypt after the first few months of protests wore out their welcome. Putin is not exactly beloved in Ukraine, but lots of Ukrainians speak Russian and a smaller portion are themselves ethnic Russian, so the country is not exactly the mass of Westward-facing Russophobes that it is sometimes portrayed to be.

And, on the third point, Ukraine's political and social divide is so problematic precisely because lots of people fall on both sides of it. We in the West sometimes like to see foreign protests as clean-cut narratives of "the people" seeking a bottom-up, Western-style liberal democracy, and there's often something to that, but it's very rarely so simple.