I kind of doubt Luke is feeling too sentimental about the saber he was holding when his hand was lopped off on what was possibly the worst day of his life. 😉
I think that’s far too simplistic a view. Regardless of what happened on the day he lost it, it was his father’s lightsaber (who did save him, his friends and the galaxy at large from the Emperor in the end), it was also given to him by Obi-wan who is now gone and Luke would have many memories of his own with it between receiving it as a “certain point of view” hand-me-down birthright, training with and using it across 3+ years up till the point it was cut from his grasp (or his grasp was cut off? 😛 ).
Sure the day he lost it was pretty traumatic but that doesn’t automatically delete any sentimental or other value Luke may put in the saber and just because he throws away and later turns down the saber again doesn’t mean he wouldn’t go back at a later time or day to pick it back up. If he really wanted to get rid of it / not see it again for all time he could have just as easily force thrown it out into the ocean when Rey first gives it to him. He mightn’t have cared for it in the moment but that still doesn’t give Rey leave to just take it.
I know in my own reality that someone turning away something I offer that is rightfully theirs doesn’t give me leave to keep it without actual consent and that same moral compass extends to our perception of character actions and motives in Star Wars, no matter how far away it’s galaxy is. The fact Luke tossed it instead of handing it back to Rey could have also meant that he didn’t want anyone to have it, another reason again that without some form of verbal consent or unmistakable sign, it wasn’t Rey’s place to just take it. That fact she did because of whatever reason doesn’t undo the wrong doing of the act itself and so this needs to be taken into consideration when looking at her character along with how she hit him in the back and threatened him with the very same saber.
I’m not saying the movie wasn’t allowed to do this but it is why one (such as myself) might see it as a reason among many others not to like Rey’s character 😉