Meaning of Warikiru?

Hello,

I am trying to understand the meaning of the word 割り切る in the context of the sentence below.

現代の若い世代の姿を見ていると、単純明快で絞り込まれた発言をする一方で、こころの中まで合理的に割り切れていないように見えます。

The dictionary tells me that the word means can't be divided, not divisible, or to give an explanation. I could understand that maybe it means "the young generation can't explain things logically anymore, it looks like". But the two meanings differ so drastically so I want to make sure the dictionary isn't wrong.

割り切る、or 割り切れる when it comes to numbers, it means it can be divided with no remainder.
When it comes to thoughts and logic, this 割り切る means to give a clear reason (to yourself) and to convince yourself that this is the right way to proceed.
So two different meanings.

And I would translate the sentence you have there as something like this:

As I observe the youths nowadays, I get the feeling that, while they voice their opinions in simplistic and well-chosen/concise words, they are not quite fully logically convinced (of their own opinions) down to their hearts.

Yes, 割り切る has multiple meanings, and I generally agree with AK, but I feel that the multiple meanings are very similar.

In the context of your Japanese sentence, the expression still does mean "separating this from that". For example, let's say you had a bad day at school but there's nothing you can do about it any more. You should be forgetting about it and be moving on in order to do better tomorrow. That is an act of warikiru. You leave that bad day behind. You separate that. That was that. Tomorrow will be another day. Right now, you may as well listen to your favorite song, or enjoy dinner with your family and watch TV. That is warikiru.

As opposed to that, an act of not being able to warikiru is, for example, to keep on thinking about that bad day. You grumble about it to a friend. You go home in a bad mood and don't smile at your family. The bad day haunts you. That's you not being able to warikiru.

We also have an expression 竹を割ったような性格 which literally means "a personality that is like a bamboo being split in half." I wonder if you've ever seen a bamboo being split by an ax. It easily splits apart very neatly. You use this expression to express people who are very clear, or straightforward, or being able to have a big argument with someone and then become friends with that someone the next minute.

So 割り切る (literally meaning completely dividing/separating) is that image.

And your sentence is talking about young people having clarity in the way they talk. But inside, they're not as clear as they seem on the outside. Their way of thinking is actually very fuzzy and blurred. Negative things linger on them. They don't know what they want. They worry about loosing friends over tiny things. They're scared they might get in trouble, and therefore avoid socializing. That's what the sentence is implying (as far as that part is concerned).

I wonder if that makes sense. The following dictionary might help too.
https://eow.alc.co.jp/search?q=%E5%89%B2%E3%82%8A%E5%88%87%E3%82%8B