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He never hated Lyle and there was no malice. From the start, he genuinely only wanted to push him to man up, get motivated, take the initative of his own life and stop moping around. It's loud, abrasive and hard-edged talk that would have worked to fire himself up if it was said to him at his lowest.
He just has trouble grasping that Lyle was a more senitive kid, shaped by a different era, family dynamic and trauma. In the First's mind there is nothing to apologize about because from his perspective everything he said was kind and encouraging, and he was struggling to understand why it wasn't having the effect he thought it would.
After Lyle went to save Aria, he completely stopped bashing him from a personal place and shifted to ribbing and bantering instead letting them start to connect a little better.
(It wasn't clearly said in the manga, but in the novels he explicitly says he enjoys bantering with Lyle the same way he does with the second because that's the way they talk in his family, and that he’s happy whenever Lyle stands up for himself and argues back).
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I’m not claiming he isn’t annoying or overly antagonistic though.
Looking back, I probably could have done a better job highlighting that side of his character in the translation.