The simple answer is that they weren't ready or obliged to. Italy had already been involved in empire building in Abyssinia and Albania (with both wars/conflicts being hugely popular), but the general staff recognized that the military wasn't ready to fight a prolonged campaign in Europe - it advised that Italy's military capabilities at best suited an offensive with a minor power such as Greece or Albania, but against a larger power should be purely defensive. While it is a fallacy of sorts that Italian war materials were old or useless in a modern conflict, the simple fact remained that they did not have enough to fully supply the military (this would play out disastrously in the eventual invasion of France). The forces were depleted of equipment, ammunition, vehicles, planes, ships, everything - quite understandable when you consider that Italy had been involved in some level of continuous armed conflict since 1923.

The Pact of Steel in 1939 (signed prior to the German invasion of Poland) was seen as a method by which Italy could forestall entry into war by at least four years - and only as a method of aligning Italy against the Anglo-French sphere. It was essentially a blank check of Italian support should Germany find itself involved in a war. The Italians did not see being called to uphold their end of the bargain so quickly, and were unprepared to respond immediately after the beginning of the war.

On a minor note, the alliance between Mussolini and Hitler wasn't as steadfast as much of popular history likes to dictate - it was an acrimonious alliance filled with both real, and perceived, backstabbing on both ends. One of these perceived backstabbings was the Molotov–Ribbentrop Pact, which Mussolini was incensed that he was not a party to. He would attempt to curry favor and alliances with Britain and France over this - but unfortunately both nations were unreceptive as Mussolini was also notoriously unreliable.

In fact, leading up to the German invasion and throughout the Phony War, Mussolini took a massive series of almost contradictory steps in order to prevent a greater outbreak of war. He would initially attempt to serve as a 'grand mediator' as he had in Munich between Germany and Poland. With this failing he would then invent language so as to neatly sidestep provisions of the pact and not be accused of cowardice or fulfilling his end of the bargain (he stressed that Italy was a "nonbelligerent" as oppossed to the unfascist and unmanly "neutral"). He would then attempt to play mediator between Germany and the allied powers, warning Holland and Belgium of Germany attack, personally counseling Hitler that peace was the 'only viable option,' before finally settling on his 'honor' demanding that Italy mobilize and enter the war so they could get their 'fair share' of the spoils (famously stating "I only need a few thousand dead so that I can sit at the peace conference as a man who has fought.”)