Socrates had a motive to welcome death, in that he believed that liberation from the corrupting influences of the body would at long last allow him to attain true knowledge. But his soul must survive his death in order for this to occur, and so he needs to convince himself that his soul is immortal. This is not easy to prove, as by its very nature it goes beyond all human experience. (This is why the proof is distinctively philosophical.) As stated in the dialogue, establishing the immortality of the soul requires "a good deal of faith and persuasive argument."
