Chemical weapons aren't why the president is interested in Syria. The US has actually been interested in helping the Syrian rebels for a long time. That last link is from the past few days, but they're all connected, which I'll get to.
The US has brought several motions to the UN. Things involving military force, military aid, or war in general are brought to the UN Security Council, a 12 member group consisting of 5 permanent members: US, UK, France, China, and Russia. The permanent members of the council have a special privilege: if any one of them vetoes a motion, it fails automatically. As I said, the US has brought several motions to the UN, which I linked above. All of them have failed, and all of them have failed because Russia (and China) have vetoed them using their veto powers.
So the US has long been interested in helping the Syrian rebels-- why is Russia concerned with vetoing efforts to help them? This is what it's all about: the politics of power. Realpolitik.
Syria, ruled by Bashar al-Assad (who functions basically as a dictator) is Russia's only ally in the Middle East region. The Russians sell a lot of arms to the Syrian government, and importantly the Russian's only naval base in the Mediterranean is based in Tartus, Syria. So, for geostrategic reasons alone, we can see that Russia is interested in keeping the friendly Syrian government in power. Though this isn't the Cold War, Russia is a competitor, so to some extent the US is interested in seeing the Syrian government fall because it would reduce the influence of a competitor in the region.
Another ally of Syria is Iran. You see, al-Assad is an Alawite-- a sect of Shiite Islam. Iran is majority Shiite Islam. The history is too long to recount here, but basically: Islam is divided into two major branches, Sunni and Shiite, which are not friends with each other. Iran and Syria are the only countries in the Middle East with Shiites in power, and Iran is the only country that actually has a majority of its citizens Shiites. It's in Iran's interest to keep the Syrian government in power, as they are the only other Shiite buddy in the region. This, too, is a reason why the US wants the Syrian government to fall; one of our longstanding goals is to remove the Iranian theocracy and prevent Iran from developing nuclear weapons. Removing a friend of Iran reduces their power and influence. Recently to this end of stopping Iran, the US has spent several years encouraging international adoption of economic sanctions against Iran.
Then, there is Israel to consider. Syria borders Israel to its north, and the two have had quite a lot of tension before; during the Six-Day War, Israel occupied the Golan Heights and effectively annexed it, in contravention of international law. The two have not been on good terms. In 2006, Israel got into a short war with its other neighbor to the north, Lebanon, during which time Syria threatened to join the war on Lebanon's side. Naturally, Israel would rather the Syrian government fall. As the US is an ally of Israel and Israel in turn provides an ally to us in the region, it's in our interest to help Israel's interest.
Looking more broadly, there are regional issues. As I mentioned earlier, Syria's government is Shiite, while the majority of the Middle East is Sunni. Another element is that the majority of Syria is also Sunni; the Shiites comprise 10-20% of Syria's population, while Sunnis are 60-70%. However, Bashar al-Assad and his father before him (also a dictator) are Alawite Shiites, and so Shiites have reigned supreme in Syria, building up resentment among the Sunni citizens because of decades-long minority rule by a group that the Sunnis consider to be heretical. This tension in the Middle East as a whole, Sunni vs. Shia, and in the country of Syria specifically, have provided sectarian lines for the population to divide themselves among. And because people in other countries want to see their particular side win, this means that foreign-based sectarian groups have rushed to help their side win the war, making it a regional proxy for the division between Sunni and Shia. Those groups, by the way, include Hezbollah, a Shia paramilitary group who has long been an enemy of Israel, as well as the Al-Nusra Front, a Sunni Islamist paramilitary group who are associates of Al-Qaeda. Obviously, this situation could easily cross borders outside of Syria and develop into a regional war. Since the US depends on the Middle East for oil, this would obviously be a bad situation for the US.
BUT WAIT! THERE'S MORE! And as always, it involves oil (and natural gas).
Qatar, a small country next to Saudi Arabia, (and coincidentally a good US ally) sought a few years ago to build a natural gas pipeline from itself up to Turkey, and from there on to Europe. Turkey (also a good US ally) was also interested in this deal, as it would make Turkey a key player in Europe's energy sector by being the transit conduit for a large component of Europe's oil and gas, which would go through the proposed Nabucco pipeline connecting Turkey to Europe. However, this all fell through. Instead, Iran, Iraq, and Syria came to a deal to transport gas from the South Pars gas field in Iran through Iraq and then to port in Syria, from where it could be sold to Europe, bypassing Turkey. The kicker? The South Pars gas field is shared between Iran and Qatar, so if Iran got a pipeline in place first, there would be no need for a pipeline from Qatar to Turkey, meaning both Qatar and Turkey don't get the money and influence they desire. So, obviously, Turkey and Qatar are interested in seeing the Syrian government change its mind, and unsurprisingly, have both condemned the Syrian government and encouraged support for the rebels. So, being that Turkey and Qatar are both allies of the US, it is once again in US interests to help their allies. But the US is interested in the Turkish-Qatari gas line for an entirely separate reason as well.
Russia is a big natural gas exporter. In fact, they supply much of Europe with its natural gas, to the point where they are a monopoly in most Eastern European countries, and double-digit percentages to France, Germany, and Italy. This dominance has also given them monopoly-pricing, which has caused friction between Russia and other European countries. In 2009, this got so bad that Russia cut all gas deliveries to Europe for 13 days, creating an energy crisis in Europe that was only resolved after Ukraine (the main country Russia's pipelines go through) basically folded to Russian demands. Now, this is obviously terrible for our European allies, as they have little or no options when it comes to Russia's demands. So, Europe has been trying to diversify its natural gas suppliers. Unfortunately, it has not done so successfully so far. Guess who was one potential supplier? That pipeline from Turkey. Europe badly needs another supplier of gas, though, so they'd likely be willing to accept gas from the Iran-Iraq-Syria pipeline even though that would involve buying gas from Iran, helping its economy. This is bad for the US, precisely because we sought economic sanctions on Iran to stop Europe from buying oil and helping its economy. So, once again it is in the United States' interest for Syria to change its mind on the pipelines. Additionally, since Russia is a rival, reducing its control over European energy markets is a strategic goal for the US in and of itself, so helping our European counterparts also helps us. Helping them, of course, means overthrowing the Syrian government.
Tl;dr The US has strategic and geopolitical reasons for needing to overthrow the Syrian government. Inevitably, this also includes trade deals regarding oil.