Play a game some time, and I think you'll understand viscerally. It is a long-time tradition (I started playing in 1963 and it was standard then) that not only marks respect for our opponents, but also serves to remind us all that it is a game. Something we play for our enjoyment. It can be pretty intense out there on the pitch, but after all , it's not the Marines hitting the beach at Iwo Jima. Does you a world of good to take the hand of a lad who a few minutes before was trying to ruck you into the mud. At least in my experience, you'll also see each team do the same for its own members - same reasoning. Then, at least if the weather is nice, it's off to the barbecue, traditionally hosted by the home side, or perhaps a stop at the pub for some laughs and a bit of story telling.
its a mark of respect for the losing team, they also normally give them three cheers.
I agree with the two answers above, but for me it symbolises 'What happens on the pitch stays on the pitch". I mean two lads can have a sever fist-fight but they'll just shake hands afterwards and maybe go for a pint and laugh about the events of the game, whereas in football that wouldn't happen, you'd just try and snap them the next game. Rugby was an amateur sport only 17 years ago, it was a past-time for doctors and lawyers and as they have been doing this for a number of years it just gets continued.
