The war in skyrim is between Nords, friends against friends, a father against a son and brother against brother. A lot of the Stormcloaks and Legion grew up and fought together. Some could be related.
It is called a Civil war because it is Nord vs Nord, the country is split. When you join the Stormcloaks every Legion soldier you kill, you're killing nords also. It isn't just Nords vs Imperials (Race)
So when Stormcloaks are trying to push out the empire, you're trying to kick nords who have lived there all their lives out, some families more than likely going back generations living in Skyrim.
But also being in the Legion, you're not just killing the enemy. Many Stormcloaks and Legion have bled together in the Great War.
It is easy for Nords to call the Empire cowards because they stopped fighting and formed a treaty. Because Nords don't really care, they have an after life that values war, death and honor of dying in combat. But there are many races involved, many innocent people who would have died if war continued. The Emperor is in no way a coward, meeting him and you would see he is far from a coward. Probably one of the most honorable people in Skyrim, him and Kodlak.
What would you have done if you were the Emperor? Your army isn't even at half strength, every city is burning and needs protection, restore order. Morale would be fairly low, battle tired, worn out. You have masses of wounded, soldiers with broken minds from the horror of war. Families torn apart and wanting to be with their husbands, brothers, sisters, fathers and mothers who are serving in the Legion. To get to the Thalmor you need to invade the Summerset Isles, which isn't even connected by land. Infact Ulfric is alive because of the treaty. The Thalmor let him escape from their prison to serve their purposes, wouldn't need him if the war was still on.
If the Stormcloak supporters can come up with a way to win the war, then I'd love to read how you'd do it. Without destroying the empire, and allowing the Thalmor to just stroll in.
You have;
Two provinces to the south that need to be secured, jungles and giant forests.
You have to make sure the Argonians don't plan to expand anymore, need to protect that border.
You don't have a full army, not even half an army left, so below half an army.
Hammerfell is occupied need to help your ally who is still your ally.
Every single city is burning, no farms would be up and running, need to feed your people.
Don't forget you need to supply your forces, since every city is in the crap hole, need to get smiths up and running.
Protection for the civilians, so roads to secure between cities so they can send supplies to each other to rebuild.
Need to place soldiers in towns because town guards would have been mostly wiped out.
Your ships also are mostly destroyed from the Naval battle in the river that surrounds the Imperial city.
Need to attack the Thalmor at the Summerset Isles who are defending their homeland now, so it'll be a battle for every inch, cities to take over, forts etc. Have to make sure you're supplied with reinforcements which would take quite sometime to get there since you have limited ships.
Or you can have peace talks, to stop further blood shed and allow soldiers (Nords, dark elves, high elves, bretons, orcs, and imperials) to return to their homes and loved ones. Rebuild your forces and repair your cities, and get money going, since war is costly. Ban the worship of Talos but never enforce it, give chests of gold to the Jarls of Skyrim, (We don't even know if these are a bribe, they could have been for lost soldiers, the fact that skyrim would of lost a lot of money as well in the war. For all we know chests were sent to Highrock also.)
That's why you need to join the ranks of the Stormcloaks... to prevent Torygg's woman from getting the throne 
