The same reason they joined the war in 1914: Germany was the primary threat and everyone was champing at the bit to get it on.
Belgian neutrality was a convenient justification.
This argument has been hashed out a thousand times before on this forum.
As well as what Stuart says, remember that politicians in the UK needed a justification. 'Gallant little Belgium' was something the public could get excited about. Germany fighting the widely loathed Russian Empire, the bogey man of the 19th century (remember the Great Game?) & with its brutality of 1904-5 still remembered, would not arouse public hatred. Rather the contrary, in fact, especially if the Germans had been better at information management & Wilhelm & Bethman-Hollweg had managed to rein in the army.
Imagine that Germany had acted in line with the line Wilhelm expressed on July 28th, when he thought there was no justification for war, & August 1st, when he wanted to step back from the brink. Imagine that he demanded & got (doubtless with the high command kicking & screaming) a defensive posture, on the grounds that he'd not lead Germany into an unjustified war, with help to Austria-Hungary only to fulfil treaty obligations if it was attacked by Russia, too big an A-H defeat being unacceptable due to the strategic position.
So, we have disrupted German mobilisation in response to Russian mobilisation. Troops accumulate at depots, & troop trains are turned round, to reinforce the east, with the western frontier getting only what it needs for defence in the case of a French attack. To be consistent with Wilhelm's statement on the 28th, Germany would not support A-H against Serbia, but would reinforce defences in Galicia when necessary - as it was. Germany doesn't declare war on anyone unless they declare war first, & attacks nobody. All this accompanied by a blizzard of telegrams to London, Paris, St. Petersburg, & anyone else thought worth talking to, & statements to the press, declaring Germany's peaceful intentions & assuring everyone it isn't going to attack anybody. It could even publicly deplore A-H policy in Serbia, A-H not being able to complain because of its need for support against Russia.
What then? Do the French attack? They're not treaty-bound to, in those circumstances. Russia wasn't a friend, merely an ally of convenience. France hosted Polish political emigres, & objected to Russia's unilateral (in violation of treaties) suppression of Polish autonomy, & Russification of Poland. A-H & to a lesser extent Germany could use that against Russia, if they'd had the wit. So if France attacks, it's a war of choice against a well-behaved Germany. How can the UK support that? Politically very, very difficult. I don't see much public support for it.
German rescue of A-H from disaster at the hands of the Russians, in a limited war, would be perfect for Germany. A limited victory, clearly German (with A-H the humiliated junior partner), & moderate concessions demanded from Russia. At most, perhaps Germany could demand the reinstatement of the Kingdom of Poland & its constitution, with Germany as a guarantor of its autonomy. How could the French & British object to that, since they'd strongly objected when Russia quashed it? Polish autonomy would be wildly popular in both Britain & France.
You see? Different behaviour by Germany could cause different behaviour by Britain, & even France. It might have stored up trouble for the future, but that's a different matter.
Edited by swerve, 16 January 2014 - 0856 AM.