Let's first define "breathe": opening a bottle of wine and letting it sit there for however long before serving it is not letting it breathe.

If you do that, the only part of the wine that has any contact with air is the surface- and that's not enough.

You've got to let air get to the rest of the wine as well, why is why pouring it into a big glass, so you can swirl it around and mix air into it, is the best way to serve it.

The only trouble with letting a wine breathe is that once air starts getting into it, that's the end of it. Old wines (forty or fifty years or so) are aged enough already to drink straight out of the bottle. Any breathing they do should be while they're in the glass and being enjoyed.

However, a young wine, or one with plenty of tannin can improve distinctly when absorbing oxygen while being decanted into a jug, and then being left for a couple of hours - the tannin softens appreciably and lets you taste the fruit in the wine much more.