It's in men's best interest to perpetuate the idea that the sexes are different, especially when they've positioned themselves as always right, so I don't think you'll get much traction trying to prove we really are mostly the same.
When it comes right down to it, if we truly communicated so differently, we'd never understand each other. Love and friendship could never develop because we'd simply not make connections. But the truth is we do make connections. "I've never felt so understood" and other similar sentiments are clearly communicated between couples all the time.
So maybe, for some, it's more a case of not learning healthy communication in the first place.