Whilst Higgs had anticipated the question, he hadn't quite anticipated the wording of it. There was something about 'doing it for her or something' that made his heart ache. He was aware that the explanation wasn't ideal. Especially since it was barely forthcoming. Nonetheless, Higgs wasn't quite sure how to explain. He did genuinely believe that in long term, he was doing Alicia a favour. It hadn't been unexpected when Weasley had informed him that she wasn't doing well, and it was hardly as if Higgs had expected Alicia to be, but... well, perhaps he had hoped she was well enough to at least accept his point of view. Higgs wasn't sure that had happened. Lydia, though, like Higgs' sister, was on the sidelines and thus perhaps more likely to see where he was coming from even if Higgs didn't provide all the information. Not for lack of wanting, but simply because he just couldn't.
Lydia's question was fair, but Higgs still wasn't convinced he knew how to answer it, so instead he sighed, staying silent for a moment. When he did finally speak again there was a strain to his voice. "I'm not in a position to make Alicia happy," he said frankly. "And I don't even feel that I'm in a position to promise her that that might change one day," he explained softly, before giving a small shrug, which wasn't meant to be dismissive but felt a little bit. "That's not fair on her," Higgs said because it wasn't. "So I asked her for a divorce," he finally concluded. As far as explanations went, it was pretty useless, but Higgs wasn't convinced he had words for something more elaborate at this point.
"I'm not sure I have a side," Higgs said frowning at Lydia. "I'm not happy with it, but I do think it's for the best," which he really, honestly and truly did.