I'm not sure you have to love them. With apologies to Raymond Carver, I'm not sure you even have to forgive them.
What you do need is a grounded understanding of why they are the way they are and how they got that way. Lesser throwaway antagonists don't require this so much. A Big Bad can't function effectively without it.
Point is, a break towards evil is a string, not a point. Barring perhaps alcohol, certain narcotics, or traumatic brain injury, readers should be able to chart a coherent course that goes beyond Well, I need an opponent for the hero, so this cardboard cutout is going to violently oppose them because...plot reasons, I guess.
In mine, the early enemy is the second husband of the protag's mother. He is, frankly, a violent, intemperate asshole direly needing to meet someone bigger, tougher, and meaner than himself - but unknown to our protag (until Part III of a four-stage arc) there's an entire backstory as to how he came to be that way. And, surprise of surprises, it's not entirely one-sided. Not all the trouble started with him, nor do all the miscalculations and transgressions bear his signature. Won't save him a beating...but he didn't just pop into the world and set about ruining lives. That his is a story of bad decisions does not negate the fact it's still a story replete with missed opportunities and at least the chance things might have gone different.
Is he an angry has-been who watched his youthful potential turn to dust and slip through his fingers? Yup. Did he once put our then-preadolescent protag in the hospital with life-threatening injuries? That, too. Does he live with the constant stress of knowing he could have been something if he'd handled it better, and now he's tied to the consequences of poor judgment? Yeah. And as a bonus, even that lousy bastard rugrat who came with his former high school sweetheart/current wife has a couple of relatives who will, in moderation, beat the ever-loving shit out of him to protect their own.
He's decently connected and borderline untouchable in his hometown. But by turns he can never be anything else, anywhere else. What life he can get he has to get on the side. The rest he just bears, much in the same way his wife occasionally has to wear long sleeves in the summer and the kid used to lie to his classmates about bike wrecks and falling out of trees.
He's the reason the protag effectively spends the first two books running. He's why the kid will, immediately after high school, push himself to the ragged edge to get away, and why his first move is buying a pawnshop shotgun and a carton of buckshot. He's the kid's rationale that maybe going to a foreign country and getting lit up by angry people with automatic weaponry is preferable to staying around the old family homestead. And he's critical to the larger story because, despite the fact he's pretty well irredeemable, he is the primary defining factor in setting the initial trajectory of the kid's life.
His fundamental sin is less his wrath than his laziness. He never made a hard decision. Never thought outside himself. Nothing he's ever lost has been a sacrifice for anything much past his own wants. A dozen times he had chances. Instead he coasted, and now it's everybody's fault but his own.
He's why the kid is what he is - and more importantly, what he's not.
Long way around saying that 'multi-dimensional' doesn't necessarily hinge on giving your hero's enemies a legitimate point so much as making sure they aren't just evil because the plot demands it, I expect.
