In Book II of Paradise Lost, Satan proposes he undertake the journey through Chaos alone. His reasons for doing so are purely self-serving. Firstly, when no one else volunteers, it makes him seem heroic in taking up the challenge. As Beelzebub says, upon the one who undertakes the journey "The weight of all and out last hope relies." Satan knows when he returns, he will gain a great deal of glory and praise from the other fallen angels. Secondly, Satan wishes to remain dominant in hell. His greatest ambition is power. Were another fallen angel to go with him, he would be forced to share the spotlight with someone else, undermining his authority and alleged heroism in undertaking such a dangerous journey.
This act is typical of Satan's character because he is egotistical. After all, his reason for rebelling against God the Father was his inability to submit to a higher authority. Even among the other fallen angels, Satan wishes to be the leader, the one most adored.