i think it's important to remember that keith canonically struggles with empathy. while he himself does experience emotions strongly and fiercely and is very disposed towards acting impulsively upon those feelings, when it comes to others, he often struggles to comprehend their emotionally driven actions.
a very good example of this is his reaction in s1e4 when pidge is planning on leaving the team to look for her lost family. keith is frustrated and confused by her decision, because it seems so illogical, objectively.
"You're putting the lives of two people over the lives of everyone in the entire galaxy."
the way keith talks to pidge here is very logically driven. what he's saying does make sense, on a completely rational basis. however, emotions aren't a rational thing - and the interesting thing is that in practice, no-one has experienced that more than keith.
we know from experience that, if keith were put in pidge's position, he would react in a very similar manner, if not with stronger unpredictability and hot-headedness, as we've seen before whenever shiro, his brother, is endangered or missing. he's intensely caring and protective over those he loves, but the realisation that others will also feel just as strongly in those kinds of situations sometimes doesn't click for him or occur to him at the time.
another example of this was in s1e13 when allura was captured by the galra very early on, and keith suggested that it may be best not to conduct the extremely dangerous mission to save her.
"Maybe we shouldn't go on this mission at all. Think about it. We'll be delivering the universe's only hope, to the universe's biggest enemy."
the others are shocked at his perceived cold and ruthless attitude, but to be perfectly fair to keith, he didn't know allura very well at the time, and i can understand him not wanting to risk all their lives, and, by extension, their mission to save the universe, for her.
after all, keith is shown throughout to have very strong core morals and values, and he is always adamant about sticking to doing what he feels is most right for something greater than himself, whether that be liberating the universe from galra control, or protecting the wellbeing of his closest loved ones. in this case, it would involve the risk of both. with his character, i can understand him feeling the need to question it, especially given the shallow nature of his relationship with allura at that point in time.
it's only when hunk asks keith whether he'd feel the same way if it were one of the paladins rather than allura who was in danger, that it does start to affect him a little, and he gets slightly defensive.
"I'm not saying I'd like the idea. I'm just thinking like a paladin."
and again, it's not that keith is uncaring - much the opposite at times, in fact, since we often see that he's probably one of the most prone to acting on his emotions out of the whole team. it's just that struggle to make the mental connection between the current situation and his own past experiences which makes it so that in the moment, it may not make sense to him as to why someone is reacting in a certain way. and this is especially the case for keith when there are conflicting moral priorities at play.
