They've both been extremely awkward from the start, it's part of their charm imo. It would also be weirder if he could smoothly and confidently express himself in a situation like this, given how he's been characterized
I actually disagree, I don't think that was supposed to be awkward, it's him being smooth, at least in Japanese high schooler standards.
Key line is page 22 which is originally 俺がいないとつまんないくせに…, you could alternatively translate it as "Even though you feel dull/bored/whatever without me..."
Naoki is by now emotionally attached to Shun, but she hadn't really understood it yet and put a lid on those emotions with this idea that I just want to see him smile, I only want to make my dear kouhai be happy. She's secretly upset that Shun's apparently enjoying the coaching better than being with her but the aforementioned facade comes first so she asks him to just leave her and go play ball full time after school.
Shun sees through this and turns it around, he's basically going 'Stop tryharding the big sis role, you're completely wrong about me, I'm no more happy playing than when I'm spending time with you. On the other hand I know all about you, you're gonna feel lonely without me'. That was 100% intentional and confident, he knows what he's doing, and he got the point across. Naoki's flustered because she realized he's spot on, she's attracted to him and Shun more or less knows.