The natural units of time are the solar day, the lunar month and the solar year. Most ancient people ended one day, and so started the next, at sunset, and started the month on the first evening the New Moon was visible. They usually started the year at or about the winter solstice or vernal equinox. So dates within a year were easy, for example the 3rd day of the 11th month. But there is no natural point to start counting years from: any year numbering system is Man-made and arbitrary.
Many ancient civilisations numbered years from events such as astronomical or meteorological phenomena or the death or accession of a King or Emperor, for example “the year after the comet”, or “three years after the whirlwind”, or “in the fifteenth year of the reign of Tiberius Caesar”. About one thousand five hundred years ago a monk called Dionysius Exiguus (Denis the Short) was making Year Tables for the date of Easter Sunday and decided to use a year numbering system starting from the year of Our Lord’s Incarnation (that is, the birth of Jesus) rather than a date associated with a pagan Roman Emperor. The years after Our Lord’s Incarnation he referred to as Anno Domini (“in the year of Our Lord”, or AD). It was however another two hundred years before his system was widely used throughout the Christian world. The Jarrow monk Bede (673 - 735) was the first writer to use it in a book, in his Ecclesiastical History of the English Church, completed in 731 (and written in Latin of course). It was only much later, after Latin had fallen out of general use, that BC (“before Christ”) began to be used for dates before the birth of Jesus.
We now believe that Dionysius made a mistake in his calculations and that Jesus was probably born about 4 BC or possibly 7 BC or a little earlier, but the numbering system he introduced has not been changed.
Jews, Christians and Moslems, and most other religions, have their own calendars and year numbering systems. In the 1950s a group of Jewish, Islamic and Christian scholars were working together in Jerusalem on those writings which are sacred to all three faiths, which Christians call the Old Testament. They all felt that their work would be a lot easier if they used a common system for dating documents and events. So in a most wonderful example of inter-faith co-operation they introduced the system now known as the Common Era, which uses as its starting point the (traditional) date of the birth of Jesus, a person who all three faiths accept as real and good. They chose this event because it led to a system similar to one with which they were all already familiar, whether or not they had used it themselves.
It is necessary and quite inoffensive to measure elapsed time forwards and backwards from a specific historical event, and the birth of Jesus is one such event although any other would do - very few people, of any faith or none, do not accept that Jesus was a real person. The problem for many people, including Jews and Moslems, is not dating an era from the historical event of the birth of Jesus but the attributes given to the person of Jesus by the use of the titles Christ and Our Lord which are incorporated into the terms AD and BC and so cannot be used by many people, including of course Jews and Moslems. Common Era has no connotations of any sort.
It is important to understand that the Common Era was originally introduced only so that a group of Jewish, Islamic and Christian scholars and historians working together could have a common system of dating documents and events common to all three faiths: it was not originally intended that it should replace all other calendars and year numbering systems. But today anyone at all, Jews, Moslems, Hindus, Sikhs, Buddhists, and of course Christians, can use it without any problems, without in any way ceasing to use their own calendars and year numbering systems, and few Christians living and working in a multi-cultural world can be offended by a system which dates things from the birth of Jesus rather than the birth of Christ.