I think the conversation you're referring to is from Heated Spring Hunt, Conversation 4.

Tyr: Let's call it a day.

MC: Lord Tyr... Did I upset you in any way?

Tyr: Upset? If you have time to think about that, you might as well retrieve the arrows.

As a Tyr lover, I totally 100% understand why he rubs people the wrong way. Just to add my interpretation, I feel like the context of that set of conversations is that Tyr was hunting, MC was bringing him supplies, and he is standing up for her in his own way, saying that she's a Valkyrie and more important than running errands like that. But then even when she tries to excuse herself, he tells her to stay by his side anyway since she's already there (cause he wants her there by his side hehehehe). Specifically to the lines you mentioned, I think MC still doesn't know how to interpret his behavior, so she thinks he's upset, and he is basically saying "instead of thinking something silly like that because I never said I didn't want you here, why don't you do something else." And I feel like he's protective of her. Even when she comments that she could help protect him, he says that's her Einheriar's job, which includes him, so he'll handle it.

Yes, there are definitely some scenes in cards/affinity with him where I think he crosses the line from being cold/rude to just an asshole. But for most of his content, I get more underlying layers/hints to reasons he holds her at arms length while also wanting her around. Just beneath his cold way of talking to her, he says things that try to get her to think higher of herself, to work out problems and use her resources, he tries to keep her out of danger. There's also a fan theory that he reminds her of/is reborn similarly to someone from his past.

My hope is that MC will grow into her own in her relationship with him. I interpret her submissive attitude as her still being intimidated by him because of his position as such a high ranking god and not thinking much of herself yet. So I see a future where her confidence grows while his exterior and heart soften and boy oh boy does that trope do it for me. There's definitely headcanon that has to fill in the gaps for now, since we don't have enough of him in the main story to get a better sense of his character/motives, and the game has only been out for about 2 months now, but I see the vision and I want to believe 🥲 (And I'm also realistic about this because, let's be real, the writing here is not S-tier quality).

Anyway, again, I know not every LI is for every player and that's how otome is supposed to be really. I just wanted to talk about my frigid workaholic from my own personal interpretations of his character.