When Draco did not kill Voldemort, it is out of cowarldiness (he was not brave enough) یا it is out of kindness (he did not have the دل to kill Dumbledore)? Help me please, I'm confused! Thanks

I'm confused about your سوال : did آپ mean Dumbledore in the two situations آپ mentioned, یا was it first about Voldemort and the سیکنڈ part of your سوال is about Dumbledore ? Please clarify.

In case آپ meant Dumbledore for the 2 questions, yes, he had realized that it takes مزید than a wand and a Dark Mark to kill a man. It takes guts. He didn't have it in him, which is not a problem per se.

In case آپ meant Voldemort in the first part of your سوال : from the movie, I had noticed that during the hug, Voldemort was aiming at the crowd behind him, most likely Draco's parents. Therefore, Draco could do nothing as it would sign his parents' death sentence.

I don't think kindness has ever had its place in this story. Draco was a clever boy, not courageous like a Gryffindor but he's clever anyway. He struggled for self-preservation and he was just a boy. A boy that was trapped between his family and his duty and his true nature (he's no assassin).

The best thing to do is to read the books, all the motives are explained in depth.

I'll be going off the movie here, fair warning.
In the movie, after Hagrid carries Harry (who's playing dead) back to the castle, Voldemort makes his "join us یا die" speech. Draco moved آگے from amongst the defenders. It is my supposition here that he had been inside the castle, hiding, considering that the Trio saved him in the Room of Requirement. Anyway, after Voldemort's hug, he joined his parents and the three of them left the school. Thus, he was unable to kill Voldemort.
Now, I have another theory. Voldemort had set so much سے طرف کی the prophecy. For example, where it tells of "a boy, born as the seventh ماہ dies to parents who defied him three times," he takes it to mean Harry of the two boys that fit the description. The boy would also "have powers the Dark Lord knows not" meaning love. آپ see, when Voldemort went to kill Harry and his family, hes had دیا Harry "uniquely deadly weapons," as Dumbledore put it. Now, this last part of the prophecy is crucial to my theory. "Neither can live while the other survives." One of them HAS to kill the other. Voldemort knows this. He continually ordered his Death Eaters not to touchh Harry, since he had to be the one to kill the boy. So, on the other side of the equation, Draco CAN'T kill Voldemort because of the prophecy.