The story of Theseus' birth has already been covered in this forum. My question is about Pittheus' motivation behind getting Aegeus drunk and offering him his daughter Aethra. In Euripedes' Medea, Aegeus describes Pittheus as 'closest of all my allies'. So why did Pittheus, who understood the Pythia's prophesy, deliberately trick Aegeus into not following the prophesy and thus cause Aegeus' death (albeit quite some time later)? What did Pittheus have to gain by this? Influence in Athens?
This is a follow-up to the accepted answer, which I think provides a good account for Pittheus' motivation, as backed up by the entry for Pittheus in The Oxford Classical Dictionary (4th edn):
[Pittheus] got [Aegeus] drunk and put him to bed with his daughter Aethra, thus becoming the grandfather of Theseus and creating a family tie between his own small state and the powerful city over the water.
How much Pittheus betrayed his ally Aegeus depends on the precise wording of the Delphic prophesy. If, as portrayed in Euripedes' Medea, the prophesy was such that Aegeus' engaging in sexual intercourse before returning home to Athens would result only in his continued childlessness (which would be consistent with Poseidon being Theseus' true father), then Pittheus' betrayal was bad enough. But if the prophesy was 'Do not loosen the bulging mouth of the wineskin until you have reached the height of Athens, lest you die of grief', then Pittheus' betrayal was complete.