Integrity in Tolkien's work and Sir Gawain poem

When reading Sir Gawain and the Green Knight for the first time I was struck by the differences in my definition of honor to the poem's. As I was reading the poem I found the knights' idea of honor to sometimes be more self-serving than what I think honor to be.

All throughout the poem, Gawain seems to be doing the "right thing" because he knows it will please those around him. He leaves Arthur's castle to find the Green Chapel because people are watching him and expect him to make good on his promise, and later he refuses to stay at the lord's castle, even though he has had such a fun time there because again people expect him to be the perfect knight and go to meet the Green Knight.

My idea of honor is doing the right thing because it is the right thing to do and not because there are people watching, integrity basically. I felt that Gawain didn't have integrity all the time and that there was an ulterior motive of keeping his reputation in front of the courts.

There are some instances in the poem that suggest that Gawain's honor wasn't completely selfish; when he refused the lord's wife and when he refused to run away before entering the Green Chapel even though he could and no one would know that he did. These instances though occur when there is only one person watching, so I think they are a much better example of his honor and integrity than openly claiming he has to leave to make his appointment like he is expected to.

I think Tolkien felt this way too because he only showcases Aragorn's honor through his actions when few are around to see him. We learn early on that he has been quietly protecting the Shire and surrounding area not expecting or wanting a reward for his deeds. There is an instance in Elowyn's halls that he states he will be going through the Paths of the Dead, but by this point, we have all these other examples of Aragorn being selfless and truly honorable that we (or I) don't see this as a call for attention but just him stating something he has to do.

I don't know if anyone else found Gawain as arrogant as I did but that was my impression during certain parts of the poem. Aragorn, though, never seemed arrogant to me because Tolkien built his character off of a foundation of selflessness right from the first meeting.