Why, and how, do some Christians and Catholics justify celebrating Easter and Christmas when the Holy Bible gives no specific dates of those events?

Propaganda was the justification.  Christians took over the Saturnalia and turned it into Christmas.  Happy Birthday Jesus!!!  But the Gospels imply a date somewhere between the end of August and the middle of September (various seasonal clues in the Gospels). As to Easter or the Resurrection it is directly related to Passover.  Passover is a day that occurs on the day of the full moon so it can be determined by astronomy.  Choosing Easter as the first Sunday following the Pascal moon is closer to making sense, than declaring Jesus was born on the day of the Saturnalia.

Were  justified by honoring God on these day's,regardless that we don't know the exact dates and God knows that.                                             How do you justify celebrating the holidays being a non believer ?

follow up question for the OP...why do you separate Christians from Catholics?  Catholics are a sect of the Christian Religions.

We Celebrate because unlike some faiths we have character. Why would it be important to celebrate on a certain day? As a matter of fact not all Christians celebrate on the same day and the same way. The day is not important, celebration of our Savior's life is. Birthdays are mention in the Bible. Dogs are mentioned as well usually as being unclean. Should you give up a dog. Do you take a picture or create video. Forbidden. Siesta? Beheading. Should we celebrate a Bar Mitzvah? Do you criticize the Jews for celebrating the birth of the Rebbe? Are you saying that the Magi and the Shepherds and the Angels singing was not a Birthday celebration.?

Basically, when Christians spread the gospel through the Mediterranean, they preached it to pagans in the Roman Empire who already had their own holidays celebrating the winter equinox. Rather than telling pagans to stop celebrating they simply had people celebrate  Jesus Birth instead of the equinox. The date for Easter is actually based on the moving  date of Passover, since in the gospels Jesus is crucified on the Friday after Passover and rises from the dead on Sunday. This is why Easter is a different date every year, since the timing of Passover is based on lunar cycles. Hope this helps.

Another objection to Easter observance made by some is that it is not  mentioned in the Bible. Some people feel we should not set apart any  day for worship unless it is specifically commanded in the Bible. Since  there is no direct example of the church celebrating the resurrection on  Easter Sunday, these people say we should not do it. Of course, there is no command in the New Testament to celebrate Jesus’ resurrection. However, neither is there a command not to  celebrate or memorialize it. Consider this. If we could only have those  religious worship times and activities that the New Testament  specifically mentions, then we would be able to do almost nothing in  terms of worship and Christian ceremony. None of the apostles are shown  to have performed a wedding ceremony or conducted a funeral, for  example. There are no examples of church services such as we have them  in our churches. But these are a part of our lives, and Christian  experience and worship. The central issue regarding Easter observance is this: How much  freedom do Christians have in the new covenant, either individually or  as a church, to express their faith, worship and thanks toward Christ in  forms not found in the Bible? Are Christians free to innovate in  worship? May church leaders establish special days to celebrate the  great acts of salvation? True, the Bible nowhere tells us to celebrate Easter. But, as  mentioned earlier, it also nowhere says not to celebrate the  resurrection of Jesus on this day. The fact is, the Bible gives examples  where God permitted human beings to set up times and forms of worship  other than what he specifically commanded. When Israel added Hanukkah and Purim to its religious calendar –  events that celebrated God’s saving acts in Jewish history – these were  acceptable to God. Jesus attended temple worship during Hanukkah, then  called the Feast of Dedication (http://biblia.com/bible/niv/John%2010.22). The Jews added the synagogue and its traditions, and nowhere is this said to be displeasing to God. In http://biblia.com/bible/niv/John%207.37 it is widely recognized that Jesus made reference to the Jewish  water-drawing ceremony, which pictured the salvation they looked for.  Jesus did not condemn this ceremony but used it as a convenient vehicle  for explaining that he was the one who would bring true salvation. Examples such as these have led many Christians to conclude that the  church also has the freedom to add to its calendar festivals that  celebrate God’s redemptive acts through Jesus. Central among these is  the resurrection of Jesus, which is celebrated in the spring (http://biblia.com/bible/niv/1%20Corinthians%2015.3-4). It is not a sin to celebrate the resurrection of Jesus Christ at  Easter. Rather, it is pleasing to God to see his people worshipping  Jesus and having understanding of the meaning of his resurrection. After  all, Jesus’ resurrection should be a cause of great rejoicing and  celebration. It is our hope for eternal life. Love, not command, is what motivates many Christians to celebrate  Easter. To harshly judge those who choose to practice their faith in  this spirit of devotion conflicts with many New Testament principles.  The fact that non-Christians or even some Christians celebrate Easter in  a secular manner only or, perhaps even in a profane way, is no reason  to avoid worshipful celebration during the Easter season. If some  celebrate during Easter in a wrong way, this is not the problem of the  season but of the people who celebrate it in a wrong manner. Just as  some may need to put "Christ back into Christmas," others may also need  to put Jesus back into Easter. We encourage all those who celebrate Easter to make Christ the center  of their celebration. The decision to observe Easter, and how to  observe it, is a personal matter. http://www.gci.org/church/holidays/easter See also: http://www.gci.org/church/holidays/christmassin

We have no doubt about the birth of Jesus Christ,  His Crucifixion, His death, and His resurrection from the dead.   So we have all rights to celebrate them.    Exact dates are quite irrelevant to us. I am a Christian Catholic.

A better question might be why are these holidays put on the same dates as pagan holidays? Ask the Catholic church that. We actually can figure out the date of the Crucifixion fairly accurately by looking at the account in the bible. It was around the time of the pagan holiday Ishtar/Easter, while the birth of Christ is no where near December 25th.

By making up excuses? The thing is that God can't possibly be pleased about the fact that the church not only attached a random date to his birthday and death but that these dates were originally pagan festivals and were only given a "Christian" meaning to attract more pagans to the church..it's all about motive I suppose. The three wise men were sent to kill Jesus not to celebrate his birth and the Jews viewed birthdays as pagan. Furthermore Christmas celebrations all over the world seem to be more about presents and trees than about Jesus. As with regards to his death..yes we should commemorate that but on the correct date (which is the same date as the Jewish passah) and without the bunnies and eggs...