There are a variety of reasons why people, particularly conservative Christians, object to the celebration of Halloween. Among other things, they see it connected to various holidays connected with the dead and debate whether such messages should be embraced lightly by children.
All Hallows EveHalloween itself descends directly from the Catholic All Hallows Eve, which is the night before All Saints Day, also known as All Hallows. This is a solemn celebration of all the saints.
SamhainAll Hallows Eve appears to have been moved in the liturgical calendar from May to October. The motivation for this is unclear, although attempts to associate it with certain pagan cultures' celebration of holidays, including the Celtic Samhain, is a popular theory.
Samhain is primarily a harvest festival. It was celebrated at the end of harvest. As such, it was not scheduled for a particular day, although the harvest generally ended around the end of October or beginning of November. This is a time when perishable goods were eaten and animals were slaughtered before they started having to cut into winter stores.
Contrary to some anti-Halloween propaganda, Samhain was not a celebration of a Celtic death god named Samhain. Such a figure does not even exist.
Day of the DeadOriginating in Mexico but now celebrated in many Hispanic and Latino communities, the Day of the Dead is a fusion of Catholic and indigenous celebrations, particularly those of the Aztecs.
The original celebration encompassed much of the month of August. After Christian conquest, the celebrations were moved to correspond with the Catholic All Saints Day (Nov. 1) and All Souls Day (Nov 2).
The Day of the Dead is both a memorial and a celebration. Today, people bear fake skulls (Aztecs used real ones) and make candy skulls out of sugar. There is feasting, parading and dancing involving a variety of brightly decorated objects. Offerings are made at graves and private shrines.
People of European descent often find the celebrations strange because their own memorials – funerals, visiting of graves, celebrations of war dead such as the American Memorial Day, and so forth - of the dead are generally solemn affairs. Frivolity is often viewed as disrespectful. For Day of the Dead celebrants, however, enjoying the things the deceased once enjoyed is part of the process of honoring them.
European FolkloreThe practice of dressing in costumes and carving faces into vegetables originates in European folklore dating back to the Middle Ages. While many online sources insist these practices are part of Celtic paganism, there is no evidence specifically linking one to the other.
European Christians have been doing these practices for centuries, warding off evil spirits and demons. This may have been at least influenced by the idea of Samhain being a time of strong connection between this world and the otherworld.
Medieval Europeans also frequently left gifts of food out to appease the spirits. They did not give gifts to children. What they did do is go from house to house on All Hallows Eve offering prayers for the dead, and in return they would be given what were known as soul cakes.
The idea of threatening tricks for treats was actually more connected with Christmas, which has historically been a time of merrymaking more than serious religious celebration.
Harvest Festivals and the DeadAutumn is a logical time to celebrate the dead. At this point, the harvest is in-progress or just finishing. While people have been able to eat fresh food all summer, now the crops are dying and people will be dependent on whatever they have stored for winter. The world itself is dying, and so cultures may also recognize this time as connected with the passing of human life as well.
As such, even when we do have evidence of a pagan culture celebrating something at this time, that doesn't mean the current celebrations have any sort of direct descent from those pagan celebrations. Many separate cultures can independently create similar celebrations.