I think their issue was actually pretty normal and expected
I mean, I think it was normal for him to probably have his bottled up feelings come out like that after being careful and proper for so many years. And as he meet the FL I think it was hinted heavily that he was slowly changing back to being impulsive, and the explosion was just something that was supposed to happen I don't think it was insecurity, it was definitely a valid worry.
As for the FL, the reaction was not the best but as she mentioned a few times she is selfish. Before she worries about the ML feelings she goes first. And the was she went about just barrelling through all the issues with his ex and the dad of his ex, plus her dad. To be questioned by the person you were fighting all that for, makes one wary, stop, and think... Rather than what she has been doing by following her feelings.
... though maybe the set up was probably not properly handled or timed. So I think it was a narrative issue rather than the story one.
And as iKdrama mentioned they didn't even break up. And if you compare this drama to other 95% Kdrama where the leads break up for "noble" stupid sacrifice and get together after a time lapse, the usual Kdrama formula. Something ind the rain was just that, and it was unsatisfying ending.
But if you are looking for dramas with no break ups. Then Love O2O is probably the first drama I could think of. It's a Chinese one.
For Kdrama, maybe try: a Poem A Day and Plus Nine Boys. But I guess they didn't need break up right at penutilate because being together after the big rejection/betrayal was the main narrative ... (?)