Why would cephalic trim be performed on already pinched tip? (Photo)

Of course, you didn't post a full set of angles, and full-face images are needed for a true evaluation, but from the frontal view, it seems your nose might be long, with the tip pointing down. And from the base view, it seems your nose might be strong in its forward projection away from your face.If that's true, there might be some help for the breathing. In general, if the tip is elevated, and "de-projected" (brought back closer to the face), those changes tend to open up the airway.When it comes to the 3mm strip, generally, there needs to be a "reason" for doing anything in a rhinoplasty. But back to the length and projection: if you think the length and projection of your nose are currently fine, then the changes I described above aren't available to help with the breathing.
How *much* to elevate the tip, or deproject the nose? We figure that out with morphs, well before surgery. I'd love for you to see some excellent professionally-designed morphs of what could possibly be done with your nose. Morphs could also help you identify what's bothering you, and help you set a goal for the rhinoplasty that's accurate for your tastes. Profile and three-quarter views would be particularly important in morphing your nose. (Side note: in my opinion, morphs should always be done by the surgeon, or he should direct an assistant as she makes the morphs. Morphs should be made with a constant eye to what actually *can* be done in surgery, for that particular nose, and only the surgeon has that information and judgment. Another aside: I also recommend that you not show morphs made by one surgeon to a different surgeon. If a surgeon makes his *own* morphs, you get to see whether he understands the important issues of your nose, and how your nose should be changed. But if you show the surgeon someone else's morphs, and he says "Of course I can make your nose look like that," then you don't really know if he fully understands, or even recognizes, the important changes shown in those morphs. And you don't know if he can make those changes during surgery.)
And remember that rhinoplasty is an exquisitely difficult operation to get right, and you should only have surgery if you are able to make yourself very confident in your surgeon's skills. The changes that your nose needs require advanced techniques, and skill that most plastic surgeons don't possess with expertise. For most noses, it's much better to not have surgery than to have inexpertly-performed surgery. Read my essay on how to stay out of trouble while selecting a rhinoplasty surgeon. And for those who have had previous surgery, it also discusses how to tell whether your first surgeon should be performing your revision. And it also discusses how to take photos that are best for online evaluations.

A possible explanation for what appears to be a counter-intuitive intervention is the curvature of the cartilages at the scroll area, where the lower part of the lateral wall cartilages meet with the lateral part of the tip cartilages. The curvature of the cartilages in the area can determine the pinched appearance.A pinched appearance is most frequently discussed as a result of excessive reduction of the lateral crura of the tip cartilages.  A pinched tip before and after surgery can have similar look yet completely different mechanism behind them.Because your nasal skin is thin, I suspect you surgeon wanted to create a smoother contour in the area. Unfortunately, that curvature was also helping to keep the airway open and removing it may influence the airway. It is my best guess for the approach and the unwanted effect on the airway.  The airway however can be restored by other means.From below, there is some bowing of the cartilages supporting the appear to be bowing slightly so a degree of additional support may be of help. Finally, in terms of your preference for outcome, I think there would be some benefit to have a 3D photo and simulation so that you can define you goals better. This would be the foundation to decide on technical aspects and feasibility. 

there is generally no good reason to perform maneuvers which compromise support in an already poorly supported tip.... the good news is that you do NOT have significant alar retraction because of your additional lower lateral 'cephalic trim.'I would suggest that your tip is pinched and slightly overprojected...this can be addressed with repositioning and support with a septal extension graft and possibly lateral crural strut graftinggood luck