Let me give you my take on it, which is purely personal, but might be shared by others who followed cycling during the last 25 years or so. Indeed, it is fairly independant on doping, since (as others have said) it is hard to say today whether Lance was less, more or equally doped than his contemporaries. It is however hard to believe that he never took anything. Others in the past have shown more class in admitting it (Zülle, Dufaux, Millar,...), but on the other hand, many others have shown even less class despite overwhelming evidence (Virenque, Hamilton, Landis, Valverde, Vinokourov, Ullrich,...).
That being said, the real reasons why I disliked Armstrong are the follwing ones:
- He destroyed the interest of many tours in a row by establishing a 5 min lead after just one TT and one mountain stage. The remaining two weeks were like a funeral procession to Paris. I turned to looking to the Giro, which used to be largely more exciting (note that this was already the case with Indurain, which I didn't like much either).
- Someone like Hinault or Indurain let other people win even when they were at their best. They would just follow the best climber day after day and let them win the stages while conforting their GC lead (remember the victories of, e.g. Lucho Herrera). That shows class. On the other hand, Armstrong (and before him Pantani in 1998-1999, or Basso in 2007-2008) tries to win every stage if that is possible, even when having already built an unassailable lead in GC, frustrating the whole peloton in the process by depriving them from the stage honours and bonusses. How much of this egoistic attitude is due to Armstrong himself, and how much of it is due to Bruyneel is hard to say, but it was certainly supported by both.
- A less understandable reason is that I always had a weakness for "Poulidor" type guys, who (almost) always finish second, like Zülle and Ullrich (maybe Andy Schleck is this new Poulidor...). Actually, I find myself disliking Armstrong less since he returned, maybe because he cannot destroy the race anymore.
I hope that it was a more constructive answer.