Okay, the Skyrim Civil war is nothing like the American Revolution, if memory serves me correctly the revolution had to do with America not being represented within British parliament, they also tried many peaceful solutions with the British Empire.
The 'Imperials' are not taking over Skyrim, they aren't invading. If Cyrodiil truly wanted to take over Skyrim, they would send a few Legions from Cyrodiil and High Rock, not locally recruited Auxiliary units in Skyrim. 70% of the Legionnaires are Nords, locally recruited from Skyrim.
Skyrim is also represented within the Empire's politics, through their High King and members of the Elder Council who represent Skyrim. Ulfric did not try for peaceful solutions to become independent, he killed the High King who was actually very interested in the idea of being independent. Ulfric fled back to Windhelm and declared war on the western Holds of Skyrim. He did not go to war with the Imperials, he's not dumb enough to mess with Cyrodiil, which he mentions that he can't afford an all out war with the Empire or upsetting Cyrodiil. Many Nords call Ulfric traitor and murderer. The Imperial Legion is made up of all races, not just Imperials.
Your execution in the beginning is because you were mistaken for a Stormcloak, being caught with Ulfric and his personal bodyguards. Which is why you were sentenced to death, you were mistaken for being an accessory to High Treason, which the only punishment is death. If you watch in the opening scenes, you'll hear Lokir pleading with the Stormcloaks to tell the Legionnaires that you and him are not with them. They only want the Stormcloaks. The Imperial Captain, ordered your death with the rest of them because you were mistaken for being one of them. Your name not being on the list can be one of several reasons, perhaps you were overlooked.
The Stormcloaks are fighting against many Nords, you're not sacking Imperial Cities when you join the Stormcloaks. You're killing Nords, Nord Hold Guards of two cities and overthrowing local Nordic rulers. There are no Imperial rulers in Skyrim, you also attack a neutral Nordic city because they didn't want to get involved.
Ulfric Stormcloak and his Militia consider anyone not with them to be against them, Whiterun was on no one's side, it was attacked because it didn't get involved.
Galmar: "If he's not with us, he's against us."
Ulfric: "He knows that. They all know that."
The Civil war is because Ulfric wants the Throne of Skyrim, if he cared about independence and his people first, he would of simply asked the High King to declare Skyrim's independence, which he would need the backing of the Jarls. Ulfric returned to solitude requesting an audience with the High King, he was allowed in because the entire court thought he was going to ask Torygg to make Skyrim independent. It didn't go down that way, he challenged the High King and the High King accepted because it is Nordic tradition. It is mentioned Torygg had some martial training but that mattered little because Ulfric used the Thu'um straight away. Little unfair, no?