It absolutely isn't.
We are the richest club in the world in this year. Real were for 12 years in a row. Does EPL getting some extra money this season makes that big difference on who is the biggest? Or was it the adidas deal who made the difference? If Real get a new deal with their shirt sponsor, will that make them bigger than us.
The number of fans is 1) estimation from mostly English media (and they are near as biased as Marca), 2) quite meaningless. About point (1), Real has more followers than us in Facebook, Instagram and Twitter, so the idea that we have so much more fans than them is a bit misleaded IMO. (2), most of these fans, came from countries who don't even watch football that much, but more importantly, they have no significance in club's success etc. Having a few more fans in Vietnam or Cambodgia is nice, but how does that make us bigger than Madrid? Do we have more fans in UK than Madrid in Spain? Extremely unlikely. Do we have more fans in places from where most of the players and the revenue come? Absolutely no. Real dwarfs us in Europe and South America, and so it is no surprise that most of the kids dream to play for them (or nowadays Barca), rather than United.
If we look at history, again it ain't close. They have 12 European Cups, we have 3. They have 33 league titles, we have 20. They have 4 Ballon D'Ors in Cristiano Ronaldo (won in the last 5 years), we have 4 in our entire history.
When it comes to who is the biggest, I think 2 factors are the most important (maybe, the only important ones): 1) the success/history; 2) the ability to recruit players. Claiming that Real don't lead in both of them is like that West Ham fan who might claim that they are the biggest club in England cause they have the most aggressive fans.
NB: And yep, I am done with the pointless argument.