Steinbeck illustrates physical strength, more specifically how it is negatively used due to the lack of self awareness.
The story starts out with Lennie carrying a mouse that he accidentally killed.
"'You always killed 'em.' Lennie looked sadly up at him. 'They was so little', he said apologetically' (9-10)."
Later on, Lennie fights back in self defense but he ends up causing more harm than intended.
"'What the hell you laughing at?' Lennie looked blankly at him. 'Huh?' Then Curley's rage exploded...Curley's fist was swinging when Lennie reached for it. The next minute Curley was flopping like a fish on a line, and his closed fist was lost in Lennie's hand. (62-63)
Steinbeck shows this through the character Lennie, and his unintentional abuse of his physical strength.
Nearing the end of the end of the story, Lennie mishandles a puppy while attempting to play with it, causing once again another conflict.
"'He was so little'; said Lennie. 'I was jus' playin' with him... an' he made like he's gonna bite me... an' I was gonna smack him... an'... an' I done it. An' then he was dead'" (87).
The mouse died because Lennie didn't realize the capabilities his strength carries, in addition to that he dosen't posses the ability to connect his actions to consequences. This combination is extremely hazardous and leads to greater problems as the story progresses.
At the end of the story, Lennie's final example of physical strength impacts not only the people involved, but every single person on the farm.
"'Don't you go yelling' he said, and he shook her; and her body flopped like a fish. And then she was still, for he had broken her neck" (91).
The fight did start in self defense, but quickly escalated as Lennie got more and more into it. He lost control of his actions, and again his mind was unable to register how hard he was going which resulted in another unwanted turnout.
There is only one way to stop Lennie from continuing on this hazardous cycle, and that is to kill him.
The third occurrence of Lennie's strength shows his thought process, and how he can't connect why the puppy died to how he was playing with it. Lennie obviously struggles with the amount of power he uses to accomplish things, and can't find a happy balance. This outcome was defiantly worse when compared to the other two because of the loss of a pet.
Throughout the story, each incidence of Lennie's strength progressively got more and more impactful. The final incident however was by far the most traumatic for Lennie and all of those around. It took a life of a human, which hurt not only the family and peers, but Lennie as well, because of the consequence awaiting him.
When one isn't fully knowledgeable of the physical strength they possess, it becomes dangerous to themselves, along with those all around them.
Since you can't connect Lennie's brain to his hands, he will continue down this path, causing bigger and bigger damage to those all around if something wasn't done about it. George had to put an end the cycle because he knew that Lennie was unable to understand and therefore control his strength.