no and no one ever claimed this.

Herodotus is a fine source here and i'm drawing on him.

There are a couple of reasons you can give why the Spartan main force wasn't at Thermopylae but the simple answer is it was intended as a holding pattern to give the rest of the Greeks time to arm and link up. The 300 were explicitly chosen from men whose families already had sons (hence no lines were extinguished) so that not quality was a deciding factor. However, at the time the 300 Spartans + a few thousand other greeks made the final stand (and most of the army retreated) the narrow position was already compromised as the Persians had found an alternative route around the narrow path which meant the army that held the rearguard was going to fight to the death. So essentially the Greek army that died at Thermopylae wasn't the whole force sent to defend the pass, it was the path's rearguard.

religion and festivals were one reason the Spartan main force wasn't at the battle but it wasn't why so few Greeks remained for the last day of battle where 299 Spartans were immortalized in death. They knowingly went on a suicide mission (and a prophecy foretold either sparta would loose a king in battle or her freedom) and you never throw your whole army towards a suicidal rear guard defense.

222. The allies then who were dismissed departed and went away, obeying the word of Leonidas, and only the Thespians and the Thebans remained behind with the Lacedemonians. Of these the Thebans stayed against their will and not because they desired it, for Leonidas kept them, counting them as hostages; but the Thespians very willingly, for they said that they would not depart and leave Leonidas and those with him, but they stayed behind and died with them. The commander of these was Demophilos the son of Diadromes. Bk7

so you have the 300 spartans+the main contingents of 2 other greek cities and those soldiers were not chosen as elites. So while the Thespians were brave, that contingent was hardly the second coming of the argonauts.

So few? The Greeks had thousands with a fleet supporting them.

They also needed to only defend thin fields of battle.

I gave an answer that gives some context to your question (quoting relevant passages from Herodotus) here:

http://www.reddit.com/r/AskHistorians/comments/2szwcc/why_300_spartans_at_the_battle_of_thermopylae/

300 was the number of the King's bodyguard, so you could consider them elite in that sense. Herodotus mentions the actual selection criteria for them as being fathers to sons though (as mentioned elsewhere here). The other greek forces we don't really know, but it does seem a more martial than average thing to do.

In terms of why so few were chosen - essentially because it was a delaying action to give the greeks time to mobilise (according to Herodotus). The full force of Spartans were unavailable until they finished celebrating the Carneia, and the other greeks were apparently delayed by the olympics.

Also reading between the lines in Herodotus (if he can be believed), Leonidas may have intended to die in order to fulfil a delphic prophecy. The prophecy said either Sparta would fall or a spartan king would die. So by the logic of the prophecy, if he died Sparta was presumably saved.