he shouldn't have run to the empire, I mean, I go out of my way to join the stormcloaks (a means to an end) and then I march up to my jarl (as his thane) and gave him the axe, full well knowing it was a request of allegiance, than he joins the empire, stupid and ignorant move.
had he sided with the stormcloaks he would have avoided conflict all together as the stormcloaks would have moved in a fortified the place entirely before the empire even knew what they were doing, yet he decided to actively seek out battle by bringing the empire in, he had a chance to avoid bloodshed, yet he chose to welcome it, I'm glad he's gone before he did something even worse.
did you hear the speech galmar and ulfric had before joining the stormcloaks? they were already planning to attack whiterun, simply for it's strategic location. whether you like their cause or not, they are going for the first punch, acting as aggressors. galmar is pretty crazy and already wants to spill blood, with his "if they're not with us, they're against us" speech. even ulfric tries to call him down for a second, but can't.
from jarl baalgruff's perspective, this is screwed up. they give him no choice but to be enemies. it's no different than if you had a home, and you knew someone was going to break in. it would piss you off. there's no decision left except to fight the burglars off or call the cops to get help. in the jarl's case, it's a whole city. why would he want to side with the people who want to attack him out of the blue? Because they're all "Nords" and "brothers" and he should realize it's for a great cause? If they were really "brothers" and it was a great cause for Nords, then Galmar wouldn't have been so bloodthirsty on his fellow Nords. he'd try to be patient, like brothers would be.