Inaction, he said, would leave al-Assad "with no reason to stop using chemical weapons."
And as the global ban against them erodes, "other tyrants" could acquire them and use them, as well against civilians and even American troops.
"If fighting spills beyond Syria's borders, these weapons could threaten allies like Turkey, Jordan and Israel. And a failure to stand against the use of chemical weapons would weaken prohibitions against other weapons of mass destruction, and embolden Assad's ally, Iran, which must decide whether to ignore international law by building a nuclear weapon or to take a more peaceful path," Obama said.
Bruce Riedel, director of the Intelligence Project at the Brookings Institution, said an indirect connection to Americans' security is a difficult case to make, "and the president is not making it."
"I don't think he can make a case, because I don't think he knows what to do," Riedel added.
3. What would be the endgame?
Obama explained the goal of military strikes. He has said the United States does not want to use the strike to take out al-Assad, institute regime change or even aid the rebels in the civil war.
"The purpose of this strike would be to deter Assad from using chemical weapons, to degrade his regime's ability to use them and to make clear to the world that we will not tolerate their use," Obama said.
Obama did say the United States could not "resolve someone else's civil war through force," and he said he would not send in American troops or pursue an open-ended war like those in Iraq or Afghanistan.
"I will not pursue a prolonged air campaign like Libya or Kosovo. This would be a targeted strike to achieve a clear objective," he said.
"Even a limited strike will send a message to Assad that no other nation can deliver," he said. "A targeted strike can make Assad, or any other dictator, think twice before using chemical weapons."
He said that "the day after any military action, we would redouble our efforts to achieve a political solution that strengthens those who reject the forces of tyranny and extremism."
Sen. Rand Paul, a Kentucky Republican and a member of the Foreign Relations Committee, told CNN after the speech that Obama did not provide a clear military objective for attacking Syria.
He said bombing the regime will not truly hold al-Assad accountable and "will create instability in the Middle East" that would leave an opening for extremist elements in Syria allied with al Qaeda.
U.S. Rep. David Valadao, R-California, agreed with Paul. "The president has failed to deliver some sort of plan that tells the American people that we can do this and this is what we are trying to accomplish," he told CNN.
4. If the U.S. attacks, what if al-Assad retaliates?
This is a major risk that concerns many members of Congress.
If the U.S. military attack is extremely limited and al-Assad retaliates, what are the contingency plans? Sen. Susan Collins, R-Maine, asked that critical question: "What if we execute this strike and then he decides to use chemical weapons again. Do we strike again?" She said it's one of her biggest concerns.
Obama did not address the contingency scenario directly, other than to say that not responding would carry unacceptable risks.
"If we fail to act, the Assad regime will see no reason to stop using chemical weapons," he said, adding that continued use could make it easier for terrorists to get their hands on them.
Al-Assad has said he would respond. "You should expect everything," he told PBS and CBS interviewer Charlie Rose.
Obama said the United States does not dismiss threats.
"But the Assad regime does not have the ability to seriously threaten our military. Any other retaliation they might seek is in line with threats that we face every day. Neither Assad nor his allies have any interest in escalation that would lead to his demise," Obama said.
5. Now that Syria welcomes diplomacy, why did Obama address the public?
Obama told CNN's Wolf Blitzer this week that he isn't convinced that Syria is telling the truth. The administration distrusts Syria and its ally Russia, and it worries that the proposal to hand over its chemical weapons stockpile is simply a tactic to buy time and derail a potential U.S. strike.