Because allowing people to vote doesn't necessarily means one needs to give them absolute power.
That's what it boils down to, ultimately. No government should ever hold absolute power over its citizens. It doesn't matter if it's an emperor in his palace or the majority in the voting booths: if a government hold absolute power, it needs to fall. Hence, governments are restrained by individual liberty.
You do have the individual right - the liberty - to participate in your country's government ; but that government must remain limited. If what you want your government to do violates the individual liberties of other people, then the government doesn't have a right to do so, and you don't have the right to make it do so.
The notion that because a democratic government derives from the will of the people it should have absolute power to enforce anything the people want is a dangerous fantasy that will turn any country into a hellhole.