Before Izuku says he's not giving up, he has these flashbacks
The first one (right) obviously referencing Iida holding his hand, the importance of how comforted he felt when that happened, and the second one (left) references chapter 57
And though both references are enough to show Izuku's mindset rn, I wonder if the rest of this scene adds into it too
Izuku hearing that Iida sees his injured left as a reminder of what he did and Izuku looks to his own hand, saying he feels the same about his own injuries
This, added in with the above panel, could mean that now that Izuku is armless, he may still see it the same way
That not only is the memory of that comfort Iida gave him enough for him to want to keep moving for the sake of others to feel the same, but his arms being gone may serve as a reminder of what he lost (physically and goal-wise, saving Tomura) and that he needs to get stronger and keep going in order to help the people who need it
Basically, Izuku being armless is not a deterrent to him. He WILL keep reaching out, even if he can't physically do it anymore