The Goat and the Lamb aren't opposites, but parallels. Meaning they most likely share more traits than not. But their differences, I suspect, lie in the thematic contrast between sheep and goats.
Sheep by nature are submissive and passive. In contrast, Goat's by nature are dominant and stubborn.
Lamb's whole thing is that they defy their nature. They didn't want to be sacrificed. They fight back instead of doing what literally everyone expects them to: sit pretty and lay down their life just because TOWW told them to.
But for Goat to defy their nature, it would have to be the opposite. It would mean Goat rolled over and took it when everyone expected them to rebel. To be a sacrificial lamb is an honor, to be a sacrificial goat (scapegoat)is a disgrace. Lamb rejected that honor and Goat presumably embraced that disgrace.
Lamb is very gentle and sweet... to their Followers. They put on a show of being a passive, kind lamb almost to an excessive extent sometimes (like how they let Midas rob them). But the submission is an act. We actually see the act drop briefly during the Fashion short when a follower puts on the Old Faith garb.
So on the flip side, we see Goat in the latest short being abrasive and mischievous. They take every chance they can to challenge or disrupt Lamb. They are, in fact, over compensating with that giant fishing pole. Because their dominance is an act.
All that to say, The Goat is fundamentally a brat.
Hello, and welcome to my Ted Talk— *gunshot*
