Einstein also thought the Cosmological Constant was correct and that an expanding universe was incorrect. Even he could be wrong,
I am one of the "sheep" that
in general prefers monitors over headphones
BUT
something needs to be pointed out in this thread, IMHumbleO. "Mixing in headphones" and "EQing in headphones" are two different animals. EQing is only a small part of mixing.
When the author asks about EQing in headphones, my response would be stick to monitors unless your monitors really suck. Even the best headphones - open or closed, "flat" or "peaked" - are going to add "unnatural" coloration to the percieved frequency response. This is due to the very nature of headphones in general. The size and proximity of the drivers combined with their de-coupling from the environment.
While it sometimes can be possible to translate from this coloration to non-proximate (i.e. non-headphone or earbud) playback, it is in general much more difficult (on good phones) to impossible (on bad phones) to make such a translation. On the other hand, an accurate translation from a great pair of 'phones is probably about as easy as it is from a pair of crapola monitors in a crapola room. In this way, I'd have to say that Dewd is not incorrect in theory.
However, in real life, I think that the chances that someone is going to have simultaneous access or budget to headphones that are better for EQ than their monitoring environment is extremely slim. Stick to the monitors for EQ.
Now, that's for EQ. "Mixing" entails many different processes, each of which can require entirely different sets of tools. EQ is just one of those many processes. For EQ, monitors may far more often than not be more appropriate than headphones, but when it comes to other aspects of "mixing" - things like setting the pan stage, creating verb tails, and low-dbFS signal processing - decent headphones can not only work just fine, but sometimes are preferable to monitors.
Also: the right tool for the right job. Someone who is engineering for majority playback on phones or buds (e.g. podcasts, mobile MP3 playback) is doing just fine mixing on phones and buds.
G.