I'm not personally offended, but I think that there are several common perceptions about the current state of the game that are part of the broader context that makes people bristle at the naming.
Within the game and metagame, several dominant archetypes are viewed as non-interactive/"not netrunner"/anti-fun. The design choices by FFG have created a perceived dominance/favoritism of some factions at the expense of others (nbn over weyland, anarch over criminal). Within the competitive scene, attendance at large events is down. Some of these may be more true than other, but these are perceptions that I see repeated on reddit, facebook, and here.
One of the things that has been a constant in ANR and has helped it to weather these storms is the maturity and inclusivity of the community and the generally civil and constructive discourse it maintains. I think that is a precious thing, and language which has the potential to alienate players (even though it may be accurate and that is not the intent) chips away at that crucial part of the game and culture.
My final point would be more appropriate to the reddit comments section (but also would get lost there). Defending the name by talking about how much the participants have given to the community and how they are dominant players/trendsetters that deserve the name "elite" is not really helping. It sounds too much like boasting or telling people that they ought to show respect to their superiors.
I'm almost done drinking my coffee so I'll wrap it up. I really appreciate the contributions to the game and the community made by the participants, and I think this is a cool idea. I think the name is accurate if potentially provocative. People are a little touchy right now because there are a number of problems in the game/metagame/community that have people worried about its future, and we should all keep this in mind when we do things to build a better world (need more coffee