Understand that what follows is me putting together pieces of the religion to answer your question; by which I mean to emphasize:
not the words of a scholar.
As you start to incorporate various verses from the Quran and narrations together, it can be noted that arrogance, as defined in the second narration, is largely considered a sin in Islam (i.e. the rejecting of the truth of the religion or holding oneself above others in station). This is likely due to the fact that the latter is an attribute of Iblis (Satan), which is seen in the Quran 7:11-13:
11. And surely, We created you [Adam] and then gave you shape, then We told the angels, “Prostrate yourselves to Adam”, and they prostrated, except Iblis [Satan], he refused to be of those who prostrated themselves.
12. (Allah) said: “What prevented you [Iblis] that you did not prostrate yourself, when I commanded you?” Iblis said: “I am better than him [Adam], You created me from fire, and him You created from clay."
13. (Allah) said: "Get down from this [paradise], it is not for you to be arrogant here. Get out, for you are of those humiliated and disgraced."
In a narration that relates to this discussion, Muhammad said:
"Allah said: Pride is my cloak and greatness My robe, and he who competes with Me in respect of either of them I shall cast into Hell-fire."
(19, Ahadith Qudsi)
Imam Nawawi again in Sharh Muslim comments on this narration:
"...What is meant is ‘Allaah says, ‘whoever seeks to compete with Me concerning them, I will punish him’.
What is meant by ‘seeks to compete with Me’ is seeking to acquire that characteristic in the sense of sharing in it.
This is a stern warning against arrogance which clearly demonstrates that it is haraam (i.e. a sin, forbidden)."
Me again:
Whereas the former, rejecting the truth of Islam, puts you outside of the fold -- and there's no coming back from rejecting the religion. Keeping this in mind, the thought process is like this:
You go to hell if you are a believer who died on the path of still committing greater sins, and then -- eventually -- are admitted to paradise.
Arrogance, as defined in the second narration, is considered to be a sin.
If you have one atom's worth of arrogance in your heart, you have died with sin in your heart.
Eventually, you will leave hell after that atom's worth or more-- and the other sins, if applicable -- are removed from your heart. Arrogance here is treated as a sin not because it resembles one but because it is one, so it is subject to the same conditions as any other sin.
To conclude this, I really appreciate your reply. It communicates that you want to have a mature discussion, and that you are willing to examine your own position honestly and critically if new information arises.