In the last episodes of season one Boku no Hero Academia, the League of Villains attacks class 1A while they are at the USJ building. A fight breaks out, and Shigaraki Tomura is about to use his quirk on Tsu's face, Midoryia jumps into action and is about to hit Shigaraki when Nomu appears in the way. The thing is, Midoryia hits Nomu with 100% of One For All and it does nothing to Nomu and there is no backlash to Midoryia's arm. I know that one of Nomu's many abilities is that he has "Absorption", which explains why it had no effect on Nomu, but what made no sense was the explanation of why it didn't affect Midoryia's arm. Midoryia thought it was because he was fighting a live being, but I immediately regard this as illogical because in season two, there are numerous occasions when he's fighting a person and he goes all out and still harms himself. This is all before he figures out how to sustain the use state of One For All at 8%(Full Cowling). So, I was wondering if someone could shed some light on this. Anything would be appreciated.
I would suspect that it is more of due to him unconsciously holding back the power of OFA.
He mentioned to All Might that he felt as if it was like an egg in the microwave which does not explode (correct me about this quote if I am wrong). An egg tends to explode in a microwave but it will not if there is not enough heat; similarly, it could be perceived that the egg is Midoriya's body while the microwave is the overwhelming power of OFA. Due to the 'microwave' not producing enough heat, which is OFA's power in this case, it also resulted in the 'egg' not exploding, which is Midoriya's bones not breaking. This thus proves the point that Midoriya was indeed holding back his power.
There are many possible explanations as to how he held back his power without knowing, but I feel that the most plausible explanation for this would be that Midoriya's adrenaline 'controlling' him. As seen in his fight with Muscular, Midoriya was somehow able to use 1,000,000% despite never using it before, and also felt no pain from his injuries. It was then mentioned by Aizawa that Midoriya was running on adrenaline. It could be possible that the rush of adrenaline he felt from almost dying by Muscular and him picturing Tsuyu dying by Shigaraki caused him to bring his power to new levels, or hold the power back from hurting him too much.
This is a fair question…
My own interpretation is that Deku's assessment of his output is not to be taken completely at face value. Compare with the related question regarding his 1 million percent output against Muscular later on in the series: How could Deku hit 1000,000% One for All punch when he had no memory of it?.
What I take away from the incident with the Nomu at USJ is that, in that crucial moment, Deku somehow found the knack of how to output his maximum power — note, not OFA's maximum power — with the constraint of not breaking his body when he releases it. After all, when All Might battles the same Nomu with "merely" the embers of OFA left within him, his blows are still on a different level compared to Deku's punch.
It's significant within the story because it shows that Deku can use OFA without breaking his body, and, crucially, he can do it in battle. Furthermore, it gives him a "sense" of what it feels like to use OFA without breaking his body, a point that he brings up later in conversation with All Might, IIRC. Importantly, Deku uses these kind of experiences to build his understanding of OFA and improve his usage of it, so it serves to setup his growth, from the standpoint of the story's progression.
(Although this might be getting tangential, the notion of developing a "sense" or "feel" for one's quirk is echoed by other characters who train Deku and his comrades, including Endeavor in season 5 of the anime. So, it's not entirely a one-off occurrence.)
Fairly simple answer, really...
Nomu's Quirk, Shock Absorption, prevented Midoriya's arm from breaking.
As Tomura Shigaraki stated, Nomu had a number of Quirks, including Super Regeneration and Shock Absorption. This means the shock from One-For-All that would usually "recoil" and destroy Midoriya's arm was completely absorbed by Nomu. The shock delivered was well within the Nomu's capacity, as seen when All Might had to strike him over 300 times at maximum capacity before subduing the villain.