Why should a Christian or a Jew be required to abandon his religion and adopt Islam?
You're question is very interesting. Let me first just point out that there are Jews and Christians who will enter Jannah, but based on their time of life.
“Verily, those who believe and those who are Jews and Christians, and Sabians, whoever believes in Allaah and the Last Day and do righteous good deeds shall have their reward with their Lord, on them shall be no fear, nor shall they grieve.” [al-Baqarah 2:62]
Before the yers of the Prophet (PBUH), anyone who followed the Prophet of his own time was on the Straight Path of salvation. So the Jews were those who followed Moosa (peace be upon him) and referred to the Tawraat for judgement at that time. When Allaah sent ‘Eesa (peace be upon him), the Children of Israel were obliged to follow him and obey him, and so they and others who followed him became Christians. When Allaah sent Muhammad (peace and blessings of Allaah be upon him), as the Final Prophet and a Messenger to all the children of Adam, all of mankind was obliged to believe in him and obey him, and refrain from what he prohibited. Those who did so are the true believers. The ummah (nation) of Muhammad (peace and blessings of Allaah be upon him) are called the believers because of their deep eemaan (faith) and conviction, and because they believe in all the past Prophets and in the prophesied events that are yet to come.
Another ayah in the Quran that can prove this:
“Surely, those who believe, those who are the Jews and the Sabians and the Christians – whosoever believed in Allaah and the Last Day, and worked righteousness, on them shall be no fear, nor shall they grieve.” [al-Maa’idah 5:69]
Therefore, there are Jews and Christians who followed their prophets during their time who will enter Jannah, God willing.
Let it just be clear that the term Jew and Christian during the times of Prophet Musa (PBUH) and Prophet 'Eeas (PBUH) do not corrolate with today's terms. Back then, these terms referred to someone who followed the book of God, and followed their messenger. I.e, they were people who worshiped God, and did not associate any partners with Him. Because of the shaytan (the devil) and because people can easily be caused to go astray, people (for example Jews and Christians) started to change the aspect of worshiping God, and started to associate partners with Him.
Keep in mind that even during the times of the Prophets, some people would not worship God, and as a result wouldn't follow the message of the Prophets, and so Allah would banish a certain town, and bring a new one instead, in essence, from scratch. But because people can be easily caused to go astray by the devil, this process would continue to happen.
A good example is in today's Christianity, Christians worship Jesus ('Easa), as the son of God (astakhfur Allah). In no way or form did Prophet 'Easa ever mention this, and never did he exert this act, but people caused this on themselves by going astray.