Sparta's refusal to join the League of Corinth made Sparta look bad. Trying to compel Sparta to join would make Macedon look bad. It was a clear diplomatic win for Philip II to let Sparta be the only Greek state to remain independent.
The Treaty of Corinth, imposed on the Greeks by Philip of Macedon in 337 BC, was not a new concept for the Greeks. For half a century, the Greek states had signed a succession of treaties that were intended to establish a "common peace" (koinĂȘ eirenĂȘ) - an end to all their current conflicts, plus a pledge to leave all other states independent. These treaties always looked like agreements between equals: all signatories agreed to a general cessation of hostilities and relinquished all claim to any other communities they had subjugated. But in fact these treaties were not signed out of a general belief in the merits of peace. Instead, they were imposed on ambitious and aggressive Greek states by the looming threat of an external guarantor - a power great enough that if it were to choose sides against any state that violated the peace, that state was sure to be quickly defeated. In effect, each common peace of the 4th century BC was a coerced ceasefire, instigated by the side that saw its chances dwindling, and enforced by a third party to that third party's benefit.
The terms of the first common peace (the so-called King's Peace of 387/6 BC) were set down by Artaxerxes II of Persia, and it was the Persians who oversaw the negotiations for further attempts to establish a common peace in 375, 371, 364, 362 and so on. Throughout the ensuing decades, the guarantor of the common peace was always Persia. They set the rules of Greek interstate relations; if any state seemed to be gathering too much power, and looked like it might become a threat to Persian interests, a common peace was soon brought about by the mere promise that Persia would throw its ships and money into the war against that state. As some Greek observers lamented, this made the Greeks effectively a dependency of the Persian empire, to which they ran for aid and arbitration whenever affairs in Greece were not going their way.
When Philip subjugated the Greeks in 337 BC, the instrument he used was nothing new; it was simply another common peace, forcing all signatories to give up their wars and conquests on pain of punishment by a powerful third party. The difference was that, for the first time, that third party was not Persia. With Macedon being indisputably the most powerful state in mainland Greece, Philip was able take on the role of arbitrator himself, instead of having to appeal to Persia. This allowed him to add an extra clause to his common peace that all Greeks could get behind: that participation in the League of Corinth required the Greek states to support his planned attack on Persia.
If this was all the Treaty of Corinth really was - another common peace, but with a different guarantor - why didn't Sparta sign? The Spartans had styled themselves champions of the King's Peace back in the 380s BC. Since their old network of unequal alliances in the Peloponnese arguably did not involve the outright subjugation of other communities (which was often defined by the raising of tribute), the terms of the peace - to leave all other Greeks independent - allowed Sparta to remain the only Greek state with significant military resources beyond its own borders. They were delighted with the terms of the Peace; they proved useful agents of the Persians, happily using the terms of the Peace as justification to attack and dissolve any upstart federation of Greek states. What had changed that made them resist the Treaty of Corinth?
The answer is simple: in 370 BC, Epameinondas of Thebes had marched an army into the Peloponnese and liberated Messenia.
Spartan control over Messenia, which dated back several centuries to a murky series of conflicts in the Archaic period, had escaped censure in the King's Peace because there was technically no independent community that the Spartans had subjugated. Nobody could represent Messenia at the negotiations for this treaty. Messenia was simply Spartan, a part of their territory since the days of their ancestors, in the same way that Athens could claim islands like Lemnos and Imbros as effectively their own land. The Spartans were safe in their control of this region and its great agricultural riches.
But once Messenia had been liberated, and a Messenian state had been created by the Thebans as a watchman on Sparta's border, Sparta's ancestral claim to the area could be reframed as the subjection of another community. This made it unacceptable under the terms of every common peace - including the Treaty of Corinth. From 370 BC onwards, therefore, Sparta stubbornly refused to sign any common peace. Doing so would imply a tacit acceptance of Messenia's claim to independence, which the Spartans could not bear. Signing any treaty that was also signed by Messenia would mean giving up their claim to this territory. So, regardless of what was happening elsewhere in the Greek world, the Spartans would not be part of any common peace, and persisted in a decades-long war against their neighbour in the vain hope of conquering it again.
With the collapse of Spartan power after the battle of Leuktra in 371 BC, its Peloponnesian League had been dissolved; the establishment of Messenia and Arkadian Megalopolis on its borders ringed Sparta with hostile states. Sparta was powerless, and its ongoing wars to reassert itself were taken by others as pointless and destabilising. Their continued claim to Messenia marginalised the Spartans in the Greek world. Their refusal to sign the Treaty of Corinth, even with its ostensibly noble purpose of fighting the Persians, made them look even worse. It was clear that the tides of the Earth had changed, and that the Spartans were living in the past. The Treaty of Corinth provided a solution to the ongoing threats and uncertainties of war with a power that was by now practically invincible. Sparta's refusal to join was selfish, delusional, obstructive and oppressive.
However, Philip II had spent decades of his career and considerable resources not just subjecting more and more of the Greek world, but also securing his legitimacy as a Greek ruler. His stated intent to attack Persia was the final propaganda coup in a sustained effort to make his state appear Greek, and to make his dominance palatable to the Greeks. Given this strategy, it would be a very bad look for Philip to try to surpress the last of the Greek states that refused to acknowledge his supremacy. Having subjected all of central and southern Greece in just a single battle at Chaironeia, he could rightly claim to have avoided unnecessary bloodshed among "his" people. It was far wiser to let stubborn, selfish Sparta be the one that seemed intent on internecine warfare for the sake of greed and lust for power. Philip didn't need Sparta; Sparta itself was neutered by its local enemies, and consumed by its obsession with regaining local ground. There was no threat in leaving Sparta independent, especially since all Sparta's enemies did sign the treaty, meaning that Macedon would be perfectly within its rights to obliterate Sparta if it chose to make a move against any member of the League of Corinth. Such a conflict would be more legitimate, and would, again, make Sparta look like it was in the wrong. Philip II was a careful diplomat and wasn't about to paint himself as a ruthless conqueror by crushing an irrelevant little backwater state just for existing in defiance of his lofty aims.